stabilization for wave equation of variable coefficients with balakrishnan taylor damping and source term abstract in this paper we consider the wave equation of variable coefficients with balakrishnan taylor damping time varying delay and source term by establishing some lyapunov functionals which are equivalent to the energy of the system and using the potential well method to deal with the source term we prove a general stability result

vibration analysis of arbitrarily shaped membranes using non dimensional dynamic influence function abstract in the present study a theoretical formulation based on the collocation method is presented for the vibration analysis of arbitrarily shaped membranes the mathematical relation between the two points of selected collocation points is given by a special function the so called non dimensional dynamic influence function unlike the collocation methods in the literature approximate functions used in this paper are simple one dimensional functions of which the only independent variable is the distance between the two points the function is also a wave type solution that satisfies exactly the given governing differential equation and physically describes the displacement reponse of a point in an infinite membrane due to a unit displacement excited at another point the approximate solution is obtained by linear superposition of non dimensional dynamic influence functions and then boundary conditions are applied at the discrete points the system matrix is always symmetric regardless of the boundary shape of the membrane and the calculated eigenvalues rapidly converge to the exact values thanks to the special function employed in this study moreover the method gives the associated mode shapes successfully without using interpolation functions between the boundary nodes the validity and efficiency of the method proposed in this paper are illustrated through several numerical examples

on the asymptotic number of edge states for magnetic schrodinger operators we consider a schrodinger operator hd a 2 with a positive magnetic field b curla in a domain 2 the imposing of neumann boundary conditions leads to the existence of some spectrum below h f b this is a boundary effect and it is related to the existence of edge states of the system we show that the number of these eigenvalues in the semi classical limit h 0 is governed by a weyl type law and that it involves a symbol on in the particular case of a constant magnetic field the curvature plays a major role

the schrodinger operator on an infinite wedge with a tangent magnetic field we study a model schrodinger operator with constant magnetic field on an infinite wedge with neumann boundary condition the magnetic field is assumed to be tangent to a face we compare the bottom of the spectrum to the model spectral quantities coming from the regular case we are particularly motivated by the influence of the magnetic field and the opening angle of the wedge on the spectrum of the model operator and we exhibit cases where the bottom of the spectrum is smaller than in the regular case numerical computations enlighten the theoretical approach

strong instability of standing waves for a fourth order nonlinear schrodinger equation with the mixed dispersions abstract in this paper we consider the strong instability of standing waves for a fourth order nonlinear schrodinger equation with the mixed dispersions i t 2 p 0 t x 0 t r n where 0 and 0 this equation arises in describing the propagation of intense laser beams in a bulk medium with kerr nonlinearity we firstly obtain the variational characterization of ground state solutions by using the profile decomposition theory in h 2 then we deduce that if 2 s u 1 0 the ground state standing wave e i t u is strongly unstable by blow up where u x n 2 u x and s is the action this result is a complement to the result of bonheure et al 2019 where the strong instability of standing waves has been studied in the case 0

blowup for fractional nls abstract we consider fractional nls with focusing power type nonlinearity i t u s u u 2 u t x r r n where 1 2 s 1 and 0 for s n 2 and 0 2 s n 2 s for s n 2 we prove a general criterion for blowup of radial solutions in r n with n 2 for l 2 supercritical and l 2 critical powers 2 s n in addition we study the case of fractional nls posed on a bounded star shaped domain r n in any dimension n 1 and subject to exterior dirichlet conditions in this setting we prove a general blowup result without imposing any symmetry assumption on u t x for the blowup proof in r n we derive a localized virial estimate for fractional nls in r n which uses balakrishnan s formula for the fractional laplacian s from semigroup theory in the setting of bounded domains we use a pohozaev type estimate for the fractional laplacian to prove blowup

applications of the direct trefftz boundary element method to the free vibration problem of a membrane in this paper the direct trefftz method is applied to solve the free vibration problem of a membrane in the direct trefftz method there exists no spurious eigenvalue however an ill posed nature of numerical instability encountered in the direct trefftz method requires some treatments the tikhonov s regularization method and generalized singular value decomposition method are used to deal with such an ill posed problem numerical results show the validity of the current approach

applications of the generalized singular value decomposition method on the eigenproblem using the incomplete boundary element formulation in this paper four incomplete boundary element formulations including the real part singular boundary element the real part hypersingular boundary element the imaginary part boundary element and the plane wave element methods are used to solve the free vibration problem among these incomplete boundary element formulations the real part singular and the hypersingular boundary elements are of the singular type and the other two are of the regular type when the incomplete formulation is used the spurious eigensolution may be encountered an auxiliary system whose boundary conditions are linearly independent of those of the original system is required in the proposed method in order to eliminate the spurious eigensolution a mathematical proof is given to show that the spurious eigensolution will appear in both the original and auxiliary systems as a result one can eliminate spurious eigensolution by means of the generalized singular value decomposition method in addition to the spurious eigensolution problem the regular boundary element formulation further suffers ill conditioned behaviors in the problem solver it is explained analytically using a circular domain why ill conditioned behaviors exist two main ill conditioned problems are the numerical instability of solution and the nonexistence of solution to solve the numerical instability of solution problem existing in these proposed regular formulations the tikhonov s regularization technique is used to improve the condition number of the leading coefficient matrix further the generalized singular value decomposition method is used to eliminate spurious eigensolutions numerical examples are given to verify the performance of these proposed methods and the results match the analytical values well

on the davey stewartson system with competing nonlinearities this paper is concerned with the blow up solutions for the davey stewartson system with competing nonlinearities which results in the loss of scaling invariance the best constant of a new gg n type inequality is given to find the sharp threshold mass of blow up and global existence moreover under the sharp threshold mass the dynamical behavior of blow up solutions is investigated including l2 concentration l2 weak limits and limiting profile

semi classical trace asymptotics for magnetic schrodinger operators with robin condition we compute the sum and number of eigenvalues for a certain class of magnetic schrodinger operators in a domain with boundary functions in the domain of the operator satisfy a magnetic robin condition the calculations are valid in the semi classical asymptotic limit and the eigenvalues concerned correspond to eigenstates localized near the boundary of the domain the formulas we derive display the influence of the boundary and the boundary condition and are valid under a weak regularity assumption of the boundary function our approach relies on three main points reduction to the boundary construction of boundary coherent states and handling the boundary term as a surface electric potential and controlling the errors by various lieb thirring inequalities

magnetic wkb constructions this paper is devoted to the semiclassical magnetic laplacian until now wkb expansions for the eigenfunctions were only established in the presence of a non zero electric potential here we tackle the pure magnetic case thanks to feynman hellmann type formulas and coherent states decomposition we develop here a magnetic born oppenheimer theory exploiting the multiple scales of the problem we are led to solve an effective eikonal equation in pure magnetic cases and to obtain wkb expansions we also investigate explicit examples for which we can improve our general theorem global wkb expansions quasi optimal agmon estimates and upper bound of the tunelling effect in symmetric cases we also apply our strategy to get more accurate descriptions of the eigenvalues and eigenfunctions in a wide range of situations analyzed in the last two decades

application of the trefftz method in plane elasticity problems direct and indirect approximations using sets of non singular complete trefftz functions i e the complete systems of solutions have been successfully applied to harmonic problems 1 in this paper the procedure is applied to a more complex situation plane elasticity problems the examples show that the present method can avoid the difficulties relating to singular integration and has good accuracy compared with traditional boundary elements

instantons and splitting in this paper we compare various formulas for the leading term of the amplitude of the splitting of the eigenvalues of semiclassical schrodinger operators with multiple wells

surface superconductivity in 3 dimensions we study the ginzburg landau system for a superconductor occupying a 3 dimensional bounded domain and improve the estimate of the upper critical field h c3 obtained by k lu and x pan in j diff eqns 168 2000 386 452 we also analyze the behavior of the order parameters we show that under an applied magnetic field lying below and not far from h c3 order parameters concentrate in a vicinity of a sheath of the surface that is tangential to the applied field and exponentially decay both in the normal and tangential directions away from the sheath in the l 2 sense as the applied field decreases further but keeps in between and away from h c2 and h c3 the superconducting sheath expands but does not cover the entire surface and superconductivity at the surface portion orthogonal to the applied field is always very weak this phenomenon is significantly different to the surface superconductivity on a cylinder of infinite height studied by x pan in comm math phys 228 2002 327 370 where under an axial applied field lying in between h c2 and h c3 the entire surface is in the superconducting state

stability of standing waves for the fractional schrodinger choquard equation abstract in this paper we consider the stability of standing waves for the fractional schrodinger choquard equation with an l 2 critical nonlinearity by using the profile decomposition of bounded sequences in h s and variational methods we prove that the standing waves are orbitally stable we extend the study of bhattarai for a single equation bhattarai 2017 to the l 2 critical case

free vibration analysis of membranes using wave type base functions the free vibration analysis of general convex polygonal membranes is carried out the selected based functions for the analysis are wave type functions which propagate in one direction and vary sinusoidally in the other direction the key feature of the present technique is to use the base functions that satisfy the governing differential equation exactly so that only the boundary conditions need to be satisfied if base functions are not chosen carefully the dependence problem of the base functions may occur and a technique to select independent base functions is suggested

application of symmetric indirect trefftz method to free vibration problems in 2d a symmetric indirect trefftz method is developed to solve the free vibration problem of a 2d membrane it is proved that in this approach the spurious eigensolution exists and an auxiliary matrix is constructed to help extraction of the spurious solution using the generalized singular value decomposition in addition to the spurious eigensolution this regular formulation suffers from its ill posed nature i e the numerical instability in order to deal with the numerical instability the tikhonov s regularization method in conjunction with the generalized singular value decomposition is suggested the proposed approach has some merits when compared with other regular boundary element formulations reported so far namely the capacity of representing eigenmodes and the ability to deal with a multiply connected domain of genus 1 several numerical examples are demonstrated to show the validity of the current approach copyright 2003 john wiley sons ltd

analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real part dual bem it has been found recently that the multiple reciprocity method mrm chen and wong engng anal boundary elements 1997 20 1 25 33 chen processings of the fourth world congress on computational mechanics onate e idelsohn sr eds argentina 1998 106 chen and wong j sound vibration 1998 217 1 75 95 or real part bem liou chen and chen j chinese inst civil hydraulics 1999 11 2 299 310 in chinese results in spurious eigenvalues for eigenproblems if only the singular ut or hypersingular lm integral equation is used in this paper a circular cavity is considered as a demonstrative example for an analytical study based on the framework of the real part dual bem the true and spurious eigenvalues can be separated by using singular value decomposition svd to understand why spurious eigenvalues occur analytical derivation by discretizing the circular boundary into a finite degree of freedom system is employed resulting in circulants for influence matrices based on the properties of the circulants we find that the singular integral equation of the real part bem for a circular domain results in spurious eigenvalues which are the zeros of the bessel functions of the second kind y k while the hypersingular integral equation of the real part bem results in spurious eigenvalues which are the zeros of the derivative of the bessel functions of the second kind yn k it is found that spurious eigenvalues exist in the real part bem and that they depend on the integral representation one uses singular or hypersingular single layer or double layer no matter what the given types of boundary conditions for the interior problem are furthermore spurious modes are proved to be trivial in the circular cavity through analytical derivations numerically they appear to have the same nodal lines of the true modes after normalization with respect to a very small nonzero value two examples with a circular domain including the neumann and dirichlet problems are presented the numerical results for true and spurious eigensolutions match very well with the theoretical prediction copyright 2000 john wiley sons ltd

global superheating field for superconductors in a large bounded interval abstract in continuation of our study of the ginzburg landau equations we study the asymptotic behavior of the superheating field for a film of width 2d in the regime small d large where is the ginzburg landau parameter using new estimates on the inner magnetic potential we improve our conditions on the parameter d and we prove that the local superheating field analyzed in our preceding paper c bolley f foucher b helffer superheating field for the ginzburg landau equations in the case of a large bounded interval j math phys 41 11 2000 7263 7289 is a global one in the regime and d large we also give accurate estimates on the superheating field

orbital stability of standing waves for schrodinger type equations with slowly decaying linear potential abstract in this paper kinds of schrodinger type equations with slowly decaying linear potential and power type or convolution type nonlinearities are considered by using the concentration compactness principle the sharp gagliardo nirenberg inequality and a refined estimate of the linear operator the existence and orbital stability of standing waves in l 2 subcritical and l 2 critical cases are established in a systematic way

profile decompositions and blowup phenomena of mass critical fractional schrodinger equations abstract we study under the radial symmetry assumption the solutions to the fractional schrodinger equations of critical nonlinearity in r 1 d d 2 with levy index 2 d 2 d 1 2 we first prove the linear profile decomposition and then apply it to investigate the properties of the blowup solutions of the nonlinear equations with mass critical hartree type nonlinearity

on the cauchy problem for the nonlinear schrodinger equations with time dependent linear loss gain abstract this paper is devoted to the cauchy problem for the nonlinear schrodinger equation with time dependent loss gain which reads i u t u u u i a t u 0 this equation appears in the recent studies of bose einstein condensates and optical systems we obtain some global existence and blow up results which depend on the size of the loss gain coefficient in particular we prove the global existence for the energy critical nonlinearity by scaling and compactness arguments we also discuss asymptotic profiles and concentration properties of blow up solutions

trefftz method for kirchhoff plate bending problems kirchhoff plate bending problems were studied by both the trefftz direct and indirect approximations in which non singular complete trefftz functions are used as the weighting and or trial functions the trefftz direct method involved only the quantities of engineering interest numerical results are given to show the efficiency and the excellent accuracy of the present method

clusters of eigenvalues for the magnetic laplacian with robin condition we study the schrodinger operator with a constant magnetic field in the exterior of a compact domain in euclidean space functions in the domain of the operator are subject to a boundary condition of the third type a magnetic robin condition in addition to the landau levels we obtain that the spectrum of this operator consists of clusters of eigenvalues around the landau levels and that they do accumulate to the landau levels from below we give a precise asymptotic formula for the rate of accumulation of eigenvalues in these clusters which is independent of the boundary condition

four and eight node hybrid trefftz quadrilateral finite element models for helmholtz problem in this paper four and eight node quadrilateral finite element models which can readily be incorporated into the standard finite element program framework are devised for plane helmholtz problems in these models frame boundary and domain approximations are defined the former is obtained by nodal interpolation and the latter is truncated from trefftz solution sets the equality of the two approximations are enforced along the element boundary both the bessel and plane wave solutions are employed to construct the domain approximation for full rankness a minimal of four and eight domain modes are required for the four and eight node elements respectively by using local coordinates and directions rank sufficient and invariant elements with minimal and close to minimal numbers of domain approximation modes are devised in most tests the proposed hybrid trefftz elements with the same number of nodes yield close solutions in absolute majority of the tests the proposed elements are considerably more accurate than their single field counterparts

eigenmode analysis of arbitrarily shaped two dimensional cavities by the method of point matching in the proposed method as in the boundary element method bem a field problem is solved on its boundary along which nodes are distributed the distinct feature of the proposed method is related to the fact that no interpolation functions between the nodes are required so that the basic collocation method is employed to satisfy a given boundary condition this approach reduces a large amount of numerical calculation induced due to the interpolation functions unlike the method of auxiliary sources mas in the proposed method only the regular functions that have finite functional values everywhere including the origins are employed as basis functions as a result the proposed method does not need the auxiliary surface the construction of which is a troublesome work because its form dimension shifting etc strongly influence the accuracy of the mas the eigenvalues calculated by the proposed method rapidly converge to the exact values thanks to the simplicity of the method moreover the method gives mode shapes successfully without using the interpolation functions between the nodes the efficiency and accuracy of the method are verified through several applications

on finite time blow up for the mass critical hartree equations we consider the fractional schrodinger equations with focusing hartree type nonlinearities when the energy is negative we show that the solution blows up in a finite time for this purpose based on glassey s argument we obtain a virial type inequality

eigenvalues of regular sturm liouville problems abstract the eigenvalues of sturm liouville sl problems depend not only continuously but smoothly on the problem an expression for the derivative of an eigenvalue with respect to a given parameter an endpoint a boundary condition a coefficient or the weight function is found

emergence of the triangular lattice near a flat wall the bifurcation of periodic solutions near a flat wall for applied magnetic fields which are slightly weaker than hc2 is considered for a reduced ginzburg landau model obtained in the large limit we formally demonstrate that following the bifurcation of the first mode when the applied magnetic field is further decreased there is a second bifurcation after which the solution develops continuously into the well known triangular lattice

numerical methods for computing ground states and dynamics of nonlinear relativistic hartree equation for boson stars efficient and accurate numerical methods are presented for computing ground states and dynamics of the three dimensional 3d nonlinear relativistic hartree equation both without and with an external potential this equation was derived recently for describing the mean field dynamics of boson stars in its numerics due to the appearance of pseudodifferential operator which is defined in phase space via symbol spectral method is more suitable for the discretization in space than other numerical methods such as finite difference method etc for computing ground states a backward euler sine pseudospectral besp method is proposed based on a gradient flow with discrete normalization and respectively for computing dynamics a time splitting sine pseudospectral tssp method is presented based on a splitting technique to decouple the nonlinearity both besp and tssp are efficient in computation via discrete sine transform and are of spectral accuracy in spatial discretization tssp is of second order accuracy in temporal discretization and conserves the normalization in discretized level in addition when the external potential and initial data for dynamics are spherically symmetric the original 3d problem collapses to a quasi 1d problem for which both besp and tssp methods are extended successfully with a proper change of variables finally extensive numerical results are reported to demonstrate the spectral accuracy of the methods and to show very interesting and complicated phenomena in the mean field dynamics of boson stars

an asymmetric indirect trefftz method for solving free vibration problems in this paper a new asymmetric indirect trefftz method aitm has been developed to solve free vibration problems the proposed method is categorized into a regular type of boundary element methods bems such that no singular or hypersingular integration is necessary however like other regular bems the proposed approach encounters the numerical instability as the number of elements increases to deal with such an ill posed behavior tikhonov s regularization method in conjunction with the generalized singular value decomposition gsvd is adopted it is proved that the degeneracy of the proposed indirect trefftz method has the same mathematical structure as the direct trefftz method thus no special effort should be paid in programming besides such an equivalency indicates that the current method does not have spurious eigensolutions furthermore the proposed approach can easily treat a multiply connected domain of genus 1 as shown in fig 1 due to its indirect nature the present approach can also represent the mode shapes within its own mathematical formulations several numerical examples are given to show the validity of the proposed approach

existence and orbital stability of standing waves for nonlinear schrodinger systems abstract in this paper we investigate the existence of solutions in h 1 r n h 1 r n for nonlinear schrodinger systems of the form u 1 1 u 1 1 u 1 p 1 2 u 1 r 1 u 1 r 1 2 u 1 u 2 r 2 u 2 2 u 2 2 u 2 p 2 2 u 2 r 2 u 1 r 1 u 2 r 2 2 u 2 under the constraints r n u 1 2 d x a 1 0 r n u 2 2 d x a 2 0 here n 1 0 i 0 r i 1 2 p i 2 4 n for i 1 2 and r 1 r 2 2 4 n this problem is motivated by the search of standing waves for an evolution problem appearing in several physical models our solutions are obtained as constrained global minimizers of an associated functional note that in the system 1 and 2 are unknown and will correspond to the lagrange multipliers our main result is the precompactness of the minimizing sequences up to translation assuming the local well posedness of the associated evolution problem we then obtain the orbital stability of the standing waves associated to the set of minimizers

sharp threshold of blow up and scattering for the fractional hartree equation abstract we consider the fractional hartree equation in the l 2 supercritical case and find a sharp threshold of the scattering versus blow up dichotomy for radial data if m u 0 s s c s c e u 0 m q s s c s c e q and m u 0 s s c s c u 0 h s 2 m q s s c s c q h s 2 then the solution u t is globally well posed and scatters if m u 0 s s c s c e u 0 m q s s c s c e q and m u 0 s s c s c u 0 h s 2 m q s s c s c q h s 2 the solution u t blows up in finite time this condition is sharp in the sense that the solitary wave solution e i t q x is global but not scattering which satisfies the equality in the above conditions here q is the ground state solution for the fractional hartree equation

pinning with a variable magnetic field of the two dimensional ginzburg landau model abstract we study the ginzburg landau energy of a superconductor with a variable magnetic field and a pinning term in a bounded smooth two dimensional domain supposing that the ginzburg landau parameter and the intensity of the magnetic field are large and of the same order we determine an accurate asymptotic formula for the minimizing energy this asymptotic formula displays the influence of the pinning term also we discuss the existence of non trivial solutions and prove some asymptotics of the third critical field

numerical study of fractional nonlinear schrodinger equations using a fourier spectral method we provide a detailed numerical investigation of dispersive schrodinger type equations involving a fractional laplacian in an one dimensional case by an appropriate choice of the dispersive exponent both mass and energy sub and supercritical regimes can be identified this allows us to study the possibility of finite time blow up versus global existence the nature of the blow up the stability and instability of nonlinear ground states and the long time dynamics of solutions the latter is also studied in a semiclassical setting moreover we numerically construct ground state solutions of the fractional nonlinear schrodinger equation

on fractional schrodinger systems of choquard type abstract in this article we first employ the concentration compactness techniques to prove existence and stability results of standing waves for nonlinear fractional schrodinger choquard equation i t a s 2 1 x n p p 2 in r n 1 where n 2 0 1 0 n s 2 2 4 n p 2 1 2 n and the constants a are nonnegative satisfying a 0 we then extend the arguments to establish similar results for coupled standing waves of nonlinear fractional schrodinger systems of choquard type the same argument works for equations with an arbitrary number of combined nonlinearities and when x n is replaced by a more general convolution potential k r n 0 under certain assumptions

fractional schrodinger equation some properties of the fractional schrodinger equation are studied we prove the hermiticity of the fractional hamilton operator and establish the parity conservation law for fractional quantum mechanics as physical applications of the fractional schrodinger equation we find the energy spectra of a hydrogenlike atom fractional bohr atom and of a fractional oscillator in the semiclassical approximation an equation for the fractional probability current density is developed and discussed we also discuss the relationships between the fractional and standard schrodinger equations

measures on double or resonant eigenvalues for linear schrodinger operator abstract in this paper we consider linear schrodinger operator with double or resonant eigenvalues the main result is the bound of the measure in a suitable space of functions of the potentials leading to such double or resonant eigenvalues namely we present measure type estimates evaluating neighborhoods of the so called double or resonant set

efficient numerical methods for computing ground states and dynamics of dipolar bose einstein condensates new efficient and accurate numerical methods are proposed to compute ground states and dynamics of dipolar bose einstein condensates becs described by a three dimensional 3d gross pitaevskii equation gpe with a dipolar interaction potential due to the high singularity in the dipolar interaction potential it brings significant difficulties in mathematical analysis and numerical simulations of dipolar becs in this paper by decoupling the two body dipolar interaction potential into short range or local and long range interactions or repulsive and attractive interactions the gpe for dipolar becs is reformulated as a gross pitaevskii poisson type system based on this new mathematical formulation we prove rigorously existence and uniqueness as well as nonexistence of the ground states and discuss the existence of global weak solution and finite time blow up of the dynamics in different parameter regimes of dipolar becs in addition a backward euler sine pseudospectral method is presented for computing the ground states and a time splitting sine pseudospectral method is proposed for computing the dynamics of dipolar becs due to the adoption of new mathematical formulation our new numerical methods avoid evaluating integrals with high singularity and thus they are more efficient and accurate than those numerical methods currently used in the literatures for solving the problem extensive numerical examples in 3d are reported to demonstrate the efficiency and accuracy of our new numerical methods for computing the ground states and dynamics of dipolar becs

helmholtz eigenvalue analysis by boundary element method abstract a new and robust scheme for the eigenvalue analysis of the helmholtz differential equation by the boundary element method bem is developed in this paper unlike the existing methods in which a highly complicated transcendental equation including the unknown wavenumbers appears the present method can reduce the computational task greatly with the help of the multiple reciprocity boundary element formulation in terms of the fundamental solution for the laplace equation and related simple calculations for polynomials the newton method is employed for determination of the desired eigenvalues two dimensional problems with various homogenous boundary conditions are solved to show the versatility of the proposed scheme

on the false degeneracy of the helmholtz boundary integral equations in this paper the false degeneracy of the helmholtz boundary integral equations is examined a new theory to explain the false degeneracy of the helmholtz boundary integral equations is given in this proposed theory a false degeneracy of the boundary integral equation is explained as finding a non trivial source distribution such that it results in trivial field quantities inside the domain interested and non trivial field quantities for its counter part i e outside the domain interested it is clearly explained that such a false degeneracy is independent of prescribed boundary conditions but dependent on the integral equation one selects moreover the false degeneracy of the integral equation for the interested domain relates to the eigenproblem for its counter part under such a unified theory the fictitious eigenvalue spurious eigenvalue and pseudo fictitious eigenvalue can be explained in a simple mathematical frame it is concluded from our theoretical analysis that a multiply connected domain results in the pseudo fictitious eigenvalue even the complex valued formulations are used in order to eliminate various kinds of false degeneracy two methods are employed according to the previous research a unified view of these two methods is provided such that they can be thought to be equivalent from mathematical point of view several numerical examples are given to show the validity of current approach

exact free vibration analysis for membrane assemblies with general classical boundary conditions abstract this paper proposes exact dynamic stiffness formulations for membranes and their assemblies under any arbitrary classical boundary conditions first by taking exact solutions in one direction satisfying all possible opposite edge supports we can derive exact general solutions of the helmholtz equation for membrane vibration then generic force and displacement boundary conditions in the other direction are expressed in terms of the general solutions finally the dynamic stiffness matrices of rectangular membrane elements are formulated which can be assembled directly and allows applications of arbitrary boundary conditions as an accurate and efficient modal solution technique the wittrick williams ww algorithm is applied onto the global dynamic stiffness matrix of the final structure the most important issue of the ww algorithm j 0 count has been resolved with the analytical expressions derived for all possible cases the proposed dynamic stiffness method dsm is then applied to several examples including individual membranes and their assemblies high accuracy and exactness of the proposed method within the whole frequency range is demonstrated by comparison with the finite element method besides interesting findings have been observed on repeated eigenvalues with distinct mode shapes corresponding to certain aspect ratio and tension ratio where physical and mathematical understanding has been provided

dependence of eigenvalues of a class of fourth order sturm liouville problems on the boundary in this paper we consider the dependence of eigenvalues of a class of fourth order sturm liouville problems on the boundary we show that the eigenvalues depend not only continuously but smoothly on boundary points and that the derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation in addition we prove that as the length of the interval shrinks to zero all higher fourth order dirichlet eigenvalues march off to plus infinity this is also true for the first i e lowest eigenvalue

remarks on the spectrum of the neumann problem with magnetic field in the half space we consider a schrodinger operator with a constant magnetic field in a one half three dimensional space with neumann type boundary conditions it is known from the works by lu pan and helffer morame that the lower bound of its spectrum is less than b the intensity of the magnetic field provided that the magnetic field is not normal to the boundary we prove that the spectrum under b is a finite set of eigenvalues each of infinite multiplicity in the case when the angle between the magnetic field and the boundary is small we give a sharp asymptotic expansion of the number of these eigenvalues

stable nucleation for the ginzburg landau system with an applied magnetic field we consider the ginzburg landau system with an applied magnetic field and analyze the behavior of solutions when the domain is a cylinder of radius overline r and the applied field is parallel to the axis it is shown that there is an upper critical value overline h such that if the modulus of the applied field is greater than overline h the normal nonsuperconducting state in which the order parameter is identically zero is stable and if the modulus of the applied field is slightly below oh the normal state is unstable in addition it is shown that there is a positive lower critical value underline h leq overline h such that the normal state is unstable if the modulus of the applied field is less than underline h and stable if the modulus is slightly above underline h in the case of type ii materials for whic h the ginzburg landau constant is large it is shown that there is a discrete set of radii such that if overline r notin cal b kappa and kappa overline r is sufficiently large then for each applied field of modulus slightly less than overline h or slightly more than underline h there is precisely one small superconducting solution up to a gauge transformation which is stable moreover for this solution the complex valued order parameter is zero only on the axis of the cylinder and its winding number is proportional to the product of 2 and the cross sectional area of the cylinder in addition the solution exhibits surface superconductivity as predicted by the physicists de gennes and st james

schrodinger operators with non degenerately vanishing magnetic fields in bounded domains we establish an asymptotic estimate of the lowest eigenvalue bf of the schrodinger operator 2 bf with a magnetic field in a bounded 2 dimensional domain where curl f vanishes non degenerately and b is a large parameter our study is based on an analysis on an eigenvalue variation problem for the sturm liouville problem using the estimate we determine the value of the upper critical field for superconductors subject to non homogeneous applied magnetic fields and localize the nucleation of superconductivity

orbital stability of solitary waves of a 3 coupled nonlinear schrodinger system abstract in this paper consideration is given to the 3 coupled nonlinear schrodinger system i t u j 2 x 2 u j i 1 3 b i j u i 2 u j 0 where u j are complex valued functions of x t r 2 j 1 2 3 and b i j are positive constants satisfying b i j b j i it will be shown first that if the symmetric matrix b b i j satisfies certain conditions then ground state solutions of the 3 coupled nonlinear schrodinger system exist and moreover they are orbitally stable the theory is then extended to include solitary waves as well in particular it will be shown that when a solitary wave is perturbed the perturbed solution must stay close to a solitary wave profile in which the translation and phase parameters are prescribed functions of time properties of these functions are then studied this is a continuous work of our previous paper where the 2 coupled nonlinear schrodinger system was considered

a new method for true and spurious eigensolutions of arbitrary cavities using the combined helmholtz exterior integral equation formulation method integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems radiation and scattering it was recently found that the real part boundary element method bem for the interior problem results in spurious eigensolutions if the singular ut or the hypersingular lm equation is used alone the real part bem results in spurious solutions for interior problems in a similar way that the singular integral equation ut method results in fictitious solutions for the exterior problem to solve this problem a combined helmholtz exterior integral equation formulation method cheef is proposed based on the cheef method the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully finally two examples for the eigensolutions of circular and rectangular cavities are considered the optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied also numerical experiments were designed to verify the analytical results it is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry while the nodal line of the rectangular is on a fixed position

threshold singularities of the spectral shift function for a half plane magnetic hamiltonian abstract we consider the schrodinger operator with constant magnetic field defined on the half plane with a dirichlet boundary condition h 0 and a decaying electric perturbation v we study the spectral shift function ssf associated to the pair h 0 v h 0 near the landau levels which are thresholds in the spectrum of h 0 for perturbations of a fixed sign we estimate the ssf in terms of the eigenvalue counting function for certain compact operators if the decay of v is power like then using pseudodifferential analysis we deduce that there are singularities at the thresholds and we obtain the corresponding asymptotic behavior of the ssf our technique gives also results for the neumann boundary condition

a meshless integration free and boundary only rbf technique based on the radial basis function rbf nonsingular general solution and dual reciprocity method drm this paper presents an inherently meshless integration free boundary only rbf collocation technique for numerical solution of various partial differential equation systems the basic ideas behind this methodology are very mathematically simple in this study the rbfs are employed to approximate the inhomogeneous terms via the drm while nonsingular general solution leads to a boundary only rbf formulation for homogenous solution the present scheme is named as the boundary knot method bkm to differentiate it from the other numerical techniques in particular due to the use of nonsingular general solutions rather than singular fundamental solutions the bkm is different from the method of fundamental solution in that the former does not require the artificial boundary and results in the symmetric system equations under certain conditions the efficiency and utility of this new technique are validated through a number of typical numerical examples completeness concern of the bkm due to the sole use of the nonsingular part of complete fundamental solution is also discussed

stability of standing waves for the fractional schrodinger hartree equation abstract in this paper we consider the stability of standing waves for the fractional schrodinger hartree equation by using the profile decomposition theory and variational methods we firstly obtain the best constant of a generalized gagliardo nirenberg inequality and then prove that the standing waves are orbitally stable

magnetic bottles in connection with superconductivity abstract motivated by the theory of superconductivity and more precisely by the problem of the onset of superconductivity in dimension two a lot of papers devoted to the analysis in a semi classical regime of the lowest eigenvalue of the schrodinger operator with magnetic field have appeared recently here we mention the works by bernoff sternberg lu pan and del pino felmer sternberg this partially recovers questions analyzed in a different context by the authors around the question of the so called magnetic bottles our aim is to analyze the former results to treat them in a more systematic way and to improve them by giving sharper estimates of the remainder in particular we improve significantly the lower bounds and as a by product we solve a conjecture proposed by bernoff sternberg concerning the localization of the ground state inside the boundary in the case with constant magnetic fields

on the blow up solutions for the nonlinear fractional schrodinger equation abstract this paper is dedicated to the blow up solutions for the nonlinear fractional schrodinger equation arising from pseudorelativistic boson stars first we compute the best constant of a gg n inequality by the profile decomposition theory and variational arguments then we find the sharp threshold mass of the existence of finite time blow up solutions finally we study the dynamical properties of finite time blow up solutions around the sharp threshold mass by giving a refined compactness lemma

harmonic oscillators with neumann condition on the half line this paper is devoted to the computation of the minimum theta 0 of the first eigenvalues for the neumann realization of harmonic oscillators on the half line we propose an algorithm to determine this minimum and we estimate the accuracy of these computations we also give numerical computations of constants appearing in superconductivity theory

boundary concentration for eigenvalue problems related to the onset of superconductivity we examine the asymptotic behavior of the eigenvalue h and corresponding eigenfunction associated with the variational problem in the regime h 1 here a is any vector field with curl equal to 1 the problem arises within the ginzburg landau model for superconductivity with the function h yielding the relationship between the critical temperature vs applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross section omega subset r 2 we first carry out a rigorous analysis of the associated problem on a half plane and then rigorously justify some of the formal arguments of bs obtaining an expansion for while also proving that the first eigenfunction decays to zero somewhere along the sample boundary when is not a disc for interior decay we demonstrate that the rate is exponential

solution of helmholtz equation by trefftz method the application of the trefftz method for calculating wave forces on offshore structures is presented indirect and direct formulations using complete and non singular systems of trefftz functions for the helmholtz equation are posed in this paper an effective technique using different interpolation functions for the velocity potential and wave force are suggested to improve the computational accuracy of the wave force the numerical examples show that the present method is highly efficient and accurate

dependence of eigenvalues of sturm liouville problems on the boundary abstract the eigenvalues of sturm liouville sl problems depend not only continuously but smoothly on boundary points the derivative of the n th eigenvalue as a function of an endpoint satisfies a first order differential equation this for arbitrary separated or coupled self adjoint regular boundary conditions in addition as the length of the interval shrinks to zero all higher eigenvalues march off to plus infinity this is also true for the first i e lowest dirichlet eigenvalue but not for the lowest neumann eigenvalue the latter has a finite limit

on the ginzburg landau critical field in three dimensions we study the three dimensional ginzburg landau model of superconductivity several natural definitions of the third critical field h governing the transition from the superconducting state to the normal state are considered we analyze the relation between these fields and give conditions as to when they coincide an interesting part of the analysis is the study of the monotonicity of the ground state energy of the laplacian with constant magnetic field and with neumann magnetic boundary condition in a domain it is proved that the ground state energy is a strictly increasing function of the field strength for sufficiently large fields as a consequence of our analysis we give an affirmative answer to a conjecture by pan 2008 wiley periodicals inc