numerical stability for a dynamic naghdi shell we consider an elastic model for a shell incorporating shear membrane bending and dynamic effects we make use of the theory proposed by arnold and brezzi 1 based on a locking free non standard mixed variational formulation this method is implemented in terms of the displacement and rotation variables as the minimization of an altered energy functional we extend this theory to the shell vibrations problem and establish optimal error estimates independent of the thickness thereby proving that shear and membrane locking is avoided we study the numerical stability both in static and dynamic regimes the approximation schemes are tested on specific examples and the numerical results confirm the estimates obtained from theory

existence of infinitely many solutions to a class of kirchhoff schrodinger poisson system in this paper we consider the existence of infinitely many solutions to following nonlinear kirchhoff schrodinger poisson system a b r 3 u 2 v x u 2 u v x u l x u f x u x r 3 l x u 2 x r 3 where constants a 0 b 0 and 0 when f has sublinear growth in u we obtain infinitely many solutions under certain assumption that v do not have a positive lower bound the technique we use in this paper is the symmetric mountain pass theorem established by kajikiya 2005

phase transition with the line tension effect we make the connection between the geometric model for capillarity with line tension and the cahn hilliard model of two phase fluids to this aim we consider the energies f eps u eps int o du 2 1 over eps int o w u lambda int bd o v u where u is a scalar density function and w and v are double well potentials we show that the behaviour of f e in the limit e 0 and depends on the limit of e log if this limit is finite and strictly positive then the singular limit of the energies f e leads to a coupled problem of bulk and surface phase transitions and under certain assumptions agrees with the relaxation of the capillary energy with line tension these results were announced in abs1 and abs2

mixed finite element methods for elastic rods of arbitrary geometry the boundary value problem for rods having arbitrary geometry and subjected to arbitrary loading is studied within the context of the small strain theory the basic assumptions underlying the rod kinematics are those corresponding to the timoshenko hypotheses in the plane rectilinear case that is plane sections normal to the line of centroids in the undeformed state remain plane but not necessarily normal the problem is formulated in both the standard and mixed variational forms and after establishing the existence and uniqueness of solutions to these equivalent problems the corresponding discrete problems are studied finite element approximations of the mixed problem are shown to be stable and convergent it is shown that the equivalence between the mixed problem and the standard problem with selective reduced integration holds only for the case of rods having constant curvature and torsion though the results of numerical experiments are presented these confirm the convergent behaviour of the mixed problem

h and d adaptive fe methods for two dimensional structural problems including post buckling of shells abstract the paper first treats the locking problem of shear elastic plates in bending in the context of multi grid methods a new plate bending element with shape functions of the allman type is presented and used for linear and non linear problems an important issue is the presentation of a flexible mesh generator with different refinement strategies according to a priori criteria different a posteriori criteria for adaptive approximations are given such as a gradient based error with one and two indicators for geometrically non linear load paths the first being residuum based and the second controlling the geometrical nonlinearities branch switching and post buckling deformation processes are investigated adaptively using these indicators and demonstrated with examples another important topic is the automatic dimensional adaptivity of beams and plates within disturbed zones as boundary layers concentrated load areas and sharp changes of thicknesses this d adaptivity is combined with h adaptivity and illustrated by some examples

notes on a group oriented setting s multisigncryption scheme with threshold designcryption zhang et al proposed recently a group oriented multisigncryption scheme with threshold designcryption and affirmed that their scheme is secure under standard complexity assumptions however the note elaborates concrete attacks on its indistinguishability and unforgeability under their security models we also provide the impossibility result of public ciphertext authenticity for the scheme

analysis of kinematic linked interpolation methods for reissner mindlin plate problems the approximation to the solution of reissner mindlin plate problem is considered in the framework of finite element techniques a general strategy involving a linking operator between rotations and vertical displacements is analyzed an abstract convergence result is provided examples of elements falling into this framework are presented and shown to be stable and locking free numerical tests detail the performances of the elements email lovadina ing unitn it

an hp error analysis of mitc plate elements we give an hp error analysis of several rectangular families of finite elements for the reissner mindlin plate bending equations we consider both the original mitc families k j bathe f brezzi and m fortin internat j numer methods engrg 28 1989 pp 1787 1801 and some new ones introduced in this paper for the deflection and rotation we give error estimates which are optimal with respect to the mesh size h and optimal up to ordo p varepsilon varepsilon 0 arbitrary with respect to the polynomial degree p we also obtain estimates for the error in the shear force calculated via two different methods our analysis utilizes some recent results of ours for the mixed method for the stokes problem as well as hp interpolation estimates for mixed methods for second order elliptic equations in this regard we derive new hp results in this paper for the brezzi douglas fortin marini spaces and improve upon previous estimates for the brezzi douglas marini spaces

preconditioners for nonconforming discretizations we prove an abstract norm equivalence for a two level method which allows us to reduce the construction of preconditioners for nonconforming finite element discretizations to known cases of conforming elements

a posteriori error analysis of the linked interpolation technique for plate bending problems we develop a posteriori error estimates for the so called linked interpolation technique to approximate the solution of plate bending problems we show that the proposed residual based estimator is both reliable and efficient

error analysis of some finite element methods for the stokes problem we prove the optimal order of convergence for some two dimensional finite element methods for the stokes equations first we consider methods of the taylor hood type the triangular p3 p2 element and the qk qk 1 i k 2 family of quadrilateral elements then we introduce two new low order methods with piecewise constant approximations for the pressure the analysis is performed using our macroelement technique which is reviewed in a slightly altered form

a stable bilinear element for the reissner mindlin plate model abstract in this paper we introduce a new quadrilateral element using isoparametric bilinear basis functions for both components of the rotation vector and the deflection the element is a stable modification of the mitc4 element we report on calculations with this new element the original mitc4 and also the bilinear element with selective reduced integration the numerical results are in accordance with the results of the numerical analysis and they show that i the method with reduced integration is highly unreliable and cannot be recommended ii the mitc4 performs rather well but its instability can lead to a decrease in accuracy for the deflection and especially to an inaccurate and oscillating shear force iii the drawbacks of the mitc4 are not present in the modified method

on the differentiability of the solution to the hamilton jacobi equation with critical fractional diffusion abstract we prove that the hamilton jacobi equation for an arbitrary hamiltonian h locally lipschitz but not necessarily convex and fractional diffusion of order one critical has classical c 1 solutions the proof is achieved using a new holder estimate for solutions of advection diffusion equations of order one with bounded vector fields that are not necessarily divergence free

existence and symmetry of solutions for critical fractional schrodinger equations with bounded potentials abstract this paper is concerned with the following fractional schrodinger equations involving critical exponents u v x u k x f u u 2 2 u in r n where is the fractional laplacian operator with 0 1 n 2 is a positive real parameter and 2 2 n n 2 is the critical sobolev exponent v x and k x are positive and bounded functions satisfying some extra hypotheses based on the principle of concentration compactness in the fractional sobolev space and the minimax arguments we obtain the existence of a nontrivial radially symmetric weak solution for the above mentioned equations without assuming the ambrosetti rabinowitz condition on the subcritical nonlinearity

a reduced constaint hp finite element method for shell problems we propose and analyze an hp finite element method for the nagdhi shell model based on rectangular elements we show that for the bending dominated case assuming sufficient smoothness on the solution the method is locking free in terms of both h and p as the thickness of the shell tends to zero our results are established under the assumption that the geometrical coefficients appearing in the model are piecewise polynomial functions

a locking free finite element method for naghdi shells abstract in this paper a locking free method using mixed finite elements is introduced to approximate the solution of naghdi shell problems with small parameter t the thickness of the shell the approach of arnold and brezzi 1997 is employed with some important changes instead of proving the discrete inf sup condition for arbitrary geometric coefficients which does not seem possible we prove a weaker stability condition for smooth enough geometrically dependent coefficients which is sufficient for deducing the optimal error estimate as long as h 2 t is uniformly bounded for extremely small t we can relax this condition either using a larger bubble space or stabilizing the problem by replacing t2 by t2 h4 in either case an optimal error estimate still holds

stabilized finite elements on anisotropic meshes a priori error estimates for the advection diffusion and the stokes problems stabilized finite elements on strongly anisotropic meshes are considered the design of the stability coefficients is addressed for both the advection diffusion and the stokes problems when using continuous piecewise linear finite elements on triangles using the polar decomposition of the jacobian of the affine mapping from the reference triangle to the current one k and from a priori error estimates a new definition of the stability coefficients is proposed our analysis shows that these coefficients do not depend on the element diameter hk but on a characteristic length associated with k via the polar decomposition a numerical assessment of the theoretical analysis is carried out

a family of c 0 finite elements for kirchhoff plates i error analysis a new finite element formulation for the kirchhoff plate model is presented the method is a displacement formulation with the deflection and the rotation vector as unknowns and it is based on ideas stemming from a stabilized method for the reissner mindlin model r stenberg in asymptotic methods for elastic structures p ciarlet l trabucho and j m viano eds de gruyter berlin 1995 and a method to treat a free boundary p destuynder and t nevers rairo model math anal numer 22 1988 pp 217 242 optimal a priori and a posteriori error estimates are derived

infinitely many solutions for a fractional kirchhoff type problem via fountain theorem abstract in this paper we use the fountain theorem and the dual fountain theorem to study the existence of infinitely many solutions for kirchhoff type equations involving nonlocal integro differential operators with homogeneous dirichlet boundary conditions a model for these operators is given by the fractional laplacian of kirchhoff type m r 2 n u x u y 2 x y n 2 s d x d y s u x u f x u in u 0 in r n where is a smooth bounded domain of r n s is the fractional laplacian operator with 0 s 1 and 2 s n is a real parameter m is a continuous and positive function and f is a caratheodory function satisfying the ambrosetti rabinowitz type condition

mixed interpolated elements for reissner mindlin plates dcpartement de mathtmatiyue l nit ersitt 1 aral quthec canado summary we present in this paper a procedure to establish reissner mindlin plate bending elements the procedure is based on the idea to combine known resuits on the approximation of stokes problems with known results on the approximation of elliptic problems the proposed elements satisfy the mathematical conditions of stability and convergence and some of them promise to provide efficient elements for practical solutions

shell deformation states and the finite element method a benchmark study of cylindrical shells abstract we demonstrate some of the basic mathematical characteristics of shell deformation states and shell models from the point of view of finite element approximation as benchmark cases we analyze in detail three simple cylindrical shell problems these problems are seemingly similar but turn out to be quite different we 1 compute the exact displacement and strain fields in the model problems both numerically and symbolically using two variants of classical shell models 2 for comparison compute numerically the displacements and strains corresponding to certain higher order dimension reduction models derived from the energy principle 3 demonstrate the dissimilarity of the three benchmark problems as to their asymptotic behaviour in the limit of zero thickness and 4 show both theoretically and experimentally how this diversity is reflected in the accuracy of standard finite element approximations of both low and high order

infinitely many solutions of a symmetric dirichlet problem here q is a bounded domain in r with smooth boundary and f i r is c and satisfies certain growth conditions if m 1 and f is an even function hence f r r is an odd function then ambrosetti and rabinowitz l 21 proved the existence of infinitely many weak solutions of d using a symmetric version of the mountain pass theorem a similar result is due to michalek 3 who considered the case where m 21 rm s c and f is invariant under a free action of the cyclic group z p on c here z p is considered as a subgroup of s c c acting essentially via scalar multiplication on c in this paper we want to investigate which kind of symmetries guarantee the existence of infinitely many solutions of d let g be a compact lie group and p g o m an orthogonal representation of g on lrm then g acts on irm via the map g x ir ir g u y gv p g v we write v for the space rm considered as a g space do there exist infinitely many solutions of d if f is invariant under this symmetry i e f gu f u for all g e g and u e v without further assumptions on p the answer to this question is no in general for example if p g id for all g e g then there is no symmetry at all and one cannot expect infinitely many solutions more generally one should exclude the existence of fixed points vg u e vi gu u for all g e g 0 our first result says that there exist infinitely many solutions of d if the following condition is satisfied

on the locking phenomenon for a class of elliptic problems in this paper we study the numerical behaviour of elliptic problems in which a small parameter is involved and an example concerning the computation of elastic arches is analyzed using this mathematical framework at first the statements of the problem and its galerkin approximations are defined and an asymptotic analysis is performed then we give general conditions ensuring that a numerical scheme will converge uniformly with respect to the small parameter finally we study an example in computation of arches working in linear elasticity conditions we build one finite element scheme giving a locking behaviour and another one which does not

existence of infinitely many large solutions for the nonlinear schrodinger maxwell equations abstract in this paper we study the nonlinear stationary schrodinger maxwell equations u v x u u f x u in r 3 u 2 in r 3 using the variant fountain theorem introduced by zou w zou variant fountain theorems and their applications manuscripta math 104 2001 343 358 under certain assumptions on v and f we get infinitely many large solutions for

normalized solutions for schrodinger poisson equations with general nonlinearities abstract in this paper we prove the existence of normalized solutions to the following schrodinger poisson equation u x 1 u 2 u f u u x r 3 r where f c r r satisfies more general conditions which cover the case f u u q 2 u with q 3 10 3 10 3 6 especially some new analytical techniques are presented to overcome the difficulties due to the presence of three terms in the corresponding energy functional which scale differently

analysis of a mixed finite element method for the reissner mindlin plate problems abstract an analysis of a triangular mixed finite element method proposed by taylor and auricchio cf 13 is presented the method is based on a linked interpolation between deflections and rotations in order to avoid the locking phenomenon cf 15 the analysis shows that the approximated deflections and rotations are first order convergent to the exact solution uniformly in the thickness

locking free finite element methods for shells we propose a new family of finite element methods for the naghdi shell model one method associated with each nonnegative integer k the methods are based on a nonstandard mixed formulation and the kth method employs triangular lagrange finite elements of degree k 2 augmented by bubble functions of degree k 3 for both the displacement and rotation variables and discontinuous piecewise polynomials of degree k for the shear and membrane stresses this method can be implemented in terms of the displacement and rotation variables alone as the minimization of an altered energy functional over the space mentioned the alteration consists of the introduction of a weighted local projection into part but not all of the shear and membrane energy terms of the usual naghdi energy the relative error in the method measured in a norm which combines the h i norm of the displacement and ro tation fields and an appropriate norm of the shear and membrane stress fields converges to zero with order k 1 uniformly with respect to the shell thickness for smooth solutions at least under the assumption that certain geometrical coefficients in the nagdhi model are replaced by piecewise constants

numerical approximation of transverse shearing stress in bent plates after a brief review of the main numerical methods for approximating the bending of plates we discuss the difficulties met in the computation of the transverse shearing stress introducing mixed variational formulations we propose several numerical schemes leading to a good approximation of this quantity finally the opportunity of using such schemes is discussed

bending dominated deformation of thin spherical shells analysis and finite element approximation in this paper the bending dominated deformation of a linearly elastic thin spherical shell is considered it is shown that the displacements converge to the solution of a constrained variational problem as the thickness of the shell tends to zero the order of the convergence is estimated and regularity results for the limit problem are derived for the numerical approximation of this limit problem a low order finite element method with a penalty term that generalizes the concept of the discrete kirchhoff triangle elements for plate bending problems is presented the application of the second strang lemma yields error estimates in the energy norm

a critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations abstract for an even functional on a banach space the symmetric mountain pass lemma gives a sequence of critical values which converges to zero under the same assumptions on the functional this paper establishes a new critical point theorem which provides a sequence of critical points converging to zero the theorem is applied to sublinear elliptic equations then a sequence of solutions converging to zero is obtained

infinitely many solutions for a class of sublinear schrodinger maxwell equations abstract in this paper we study the existence of infinitely many solutions for a class of sublinear schrodinger maxwell equations the proof is based on the variant fountain theorem established by zou recent results from the literature are extended

two finite element approximations of naghdi s shell model in cartesian coordinates we present a penalized version of naghdi s model and a mixed formulation of the same model in cartesian coordinates for linearly elastic shells with little regularity and finite element approximations thereof numerical tests are given that validate and illustrate our approach

a locking free approximation of curved rods by straight beam elements we consider an elastic model for a curved rod with arbitrary three dimensional geometry incorporating shear and membrane as well as bending and torsion effects we define an approximation procedure based on a discretization by linear timoshenko beam elements introducing an equivalent mixed problem we establish optimal error estimates independent of the thickness thereby proving that shear and membrane locking is avoided the approximation scheme is tested on specific examples and the numerical results confirm the estimates obtained by theory

high energy solutions for the superlinear schrodinger maxwell equations abstract in this paper we study the existence of infinitely many large energy solutions for the superlinear schrodinger maxwell equations u v x u u f x u in r 3 u 2 in r 3 via the fountain theorem in critical point theory

dual mixed p and hp finite elements for elastic membrane problems a complementary energy based dimensionally reduced plate model using a two field dual mixed variational principle of non symmetric stresses and rotations is derived both the membrane and bending equilibrium equations expressed in terms of non symmetric mid surface stress components are satisfied a priori introducing first order stress functions it is pointed out that i the membrane shear and bending energies of the plate written in terms of first order stress functions are decoupled ii although unmodified 3 d constitutive equations are applied the energy parts do not contain the 1 1 2 term for isotropic linearly elastic materials these facts mean that the finite element formulation based on the present plate model should be free from shear locking when the thickness tends to zero and free from incompressibility locking when the poisson ratio converges to 0 5 irrespective of low order h or higher order p elements are used curvilinear dual mixed hp finite elements with higher order stress approximation and continuous surface tractions are developed and presented for the membrane 2 d elasticity problem in this case the formulation requires the approximation of three independent variables two components of a first order stress function vector and a scalar rotation numerical performance of three quadrilateral dual mixed elements is presented and compared to displacement based hp finite elements when the poisson ratio converges to the incompressible limit of 0 5 the numerical results show that as expected the dual mixed elements developed in this paper are free from locking in the energy norm as well as in the stress computations for both h and p extensions copyright 2001 john wiley sons ltd

a uniformly accurate finite element method for the reissner mindlin plate a simple finite element method for the reissner mindlin plate model in the prim itive variables is presented and analyzed the method uses nonconforming linear finite elements for the transverse displacement and conforming linear finite elements enriched by bubbles for the rotation with the computation of the element stiffness matrix modified by the inclusion of a simple elementwise averaging it is proved that the method converges with optimal order uniformly with respect to thickness

regularity estimates for the solution and the free boundary of the obstacle problem for the fractional laplacian we use a characterization of the fractional laplacian as a dirichlet to neumann operator for an appropriate differential equation to study its obstacle problem we write an equivalent characterization as a thin obstacle problem in this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary

error analysis of some galerkin least squares methods for the elasticity equations the recent technique of stabilizing mixed finite element methods by augmenting the galerkin formulation with least squares terms calculated separately on each element is considered the error analysis is performed in a unified manner yielding improved results for some methods introduced earlier in addition a new formulation is introduced and analyzed method is used within two different contexts the first is in connection with the plain strain or three dimensional problems near the incompressible limit for which the poisson ratio equals one half it is well known that for these problems a standard lower order displacement finite element method will break down by now it is also well known how a working method can be obtained a new unknown the pressure is introduced and discretized with a finite element space different from that used for the displacements the finite element method obtained falls into the class of saddlepoint problems for which there is a general theory developed by brezzi and babuska 5 7 the application of this theory shows that the method converges optimally if the discrete spaces for the displacement and pressure satisfy a stability condition for a particular choice of displacement and pressure approximations it can be a difficult task to verify this babuska brezzi or inf sup condition during the last decade this problem has been intensively studied and the performances of many combinations are now known cf 18 and 23 26 for some recent extensions in addition there exists a general technique utilizing bubble functions by which a stable method can

an improved reissner mindlin triangular element abstract a modified version of the low order mixed finite element method proposed by onate et al internat j numer method engng 37 1994 2569 for the reissner mindlin plate model is analyzed it is proved that the new method is optimal convergent uniform in the thickness of the plate

on the construction of optimal mixed finite element methods for the linear elasticity problem the mixed finite element method for the linear elasticity problem is considered we propose a systematic way of designing methods with optimal convergence rates for both the stress tensor and the displacement the ideas are applied in some examples

locking free quadrilateral continuous discontinuous finite element methods for the reissner mindlin plate we develop a finite element method with continuous displacements and discontinuous rotations for the reissner mindlin plate model on quadrilateral elements to avoid shear locking the rotations mu

discretization by finite elements of a model parameter dependent problem the discretization by finite elements of a model variational problem for a clamped loaded beam is studied with emphasis on the effect of the beam thickness which appears as a parameter in the problem on the accuracy it is shown that the approximation achieved by a standard finite element method degenerates for thin beams in contrast a large family of mixed finite element methods are shown to yield quasioptimal approximation independent of the thickness parameter the most useful of these methods may be realized by replacing the integrals appearing in the stiffness matrix of the standard method by gauss quadratures

homoclinic solutions for fractional discrete laplacian equations abstract in this paper we introduce a variational framework to a fractional difference equation on z driven by the fractional discrete laplacian and involving a coercive weight function and a positive parameter by means of the critical point theory we prove the existence of at least two nontrivial and nonnegative homoclinic solutions for big enough

a new family of stable elements for nearly incompressible elasticity based on a mixed petrov galerkin finite element formulation adding to the classical hellinger reissner formulation another residual form of the equilibrium equation a new petrov galerkin finite element method is derived it fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations including equal order discontinuous stress and continuous displacement interpolations which are unstable within the galerkin approach error estimates are presented using the babuska brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method

a low order nonconforming finite element for reissner mindlin plates we propose a locking free element for plate bending problems based on the use of nonconforming piecewise linear functions for both rotations and deflections we prove optimal error estimates with respect to both the meshsize and the analytical solution regularity

efficient chosen ciphertext secure certificateless threshold key encapsulation mechanism abstract as a practical extension of our previous work on certificateless threshold cryptosystem this paper proposes the first direct certificateless threshold key encapsulation mechanism that inherits the same trust level of the original scheme and removes the length limitation of a traditional public key encryption security against threshold chosen ciphertext attacks are proved in a random oracle model under a new assumption it tolerates the type i adversary that can replace public keys and the type ii adversary that has access to the system s master key the implied encapsulation scheme is very efficient when compared to the most efficient schemes in a traditional public key cryptosystem and it is slightly more efficient in terms of key length and encapsulation speed when compared to the identity based cryptosystems that have the same ciphertext overhead finally we describe several potential modifications of our scheme

existence of ground state solutions for the nonlinear fractional schrodinger poisson system with critical sobolev exponent abstract in this paper we study the existence of ground state solutions for the nonlinear fractional schrodinger poisson system with critical sobolev exponent s u v x u u u q 1 u u 2 s 2 u in r 3 t u 2 in r 3 where r is a parameter 1 q 2 s 1 3 2 s 3 2 s s t 0 1 and 2 s 2 t 3 under certain assumptions on v x using the method of pohozaev nehari manifold and the arguments of brezis nirenberg the monotonic trick and global compactness lemma we prove the existence of a nontrivial ground state solution

analysis of some low order quadrilateral reissner mindlin plate elements four quadrilateral elements for the reissner mindlin plate model are considered the elements are the stabilized mitc4 element of lyly stenberg and vihinen 1933 the min4 element of tessler and hughes 1983 the q4bl element of zienkiewicz et al 1993 and the fmin4 element of kikuchi and ishii 1999 for all elements except the q4bl element a unifying variational formulation is introduced and optimal h 1 and l 2 error bounds uniform in the plate thickness are proven moreover we propose a modified q4bl element and show that it admits the optimal h 1 and l 2 error bounds uniform in the plate thickness in particular we study the convergence behavior of all elements regarding the mesh distortion

a conforming locking free approximation for a koiter shell abstract as in the naghdi framework membrane locking is expected for bending dominated koiter shell when the thickness decreases inspired by arnold and brezzi 1997 we design a locking free mixed finite element method for the koiter shell this method is implemented in terms of the displacement variables as the minimization of an altered energy over a conforming finite element space we approximate the tangential displacements by continuous piecewise polynomials augmented by bubbles and the transversal displacements by the consistent hct hsieh clough tocher element the membrane stresses derived from a partial integration of the membrane energy is approximated by discontinuous piecewise polynomials we establish optimal error estimates independent of the thickness under some restrictions which prove that the mixed solution is locking free we confirm our theoretical predictions with some numerical tests in particular we consider a hemicylindrical shell and an hyperbolic paraboloid shell

berestycki lions conditions on ground state solutions for kirchhoff type problems with variable potentials based on the strategy introduced by chen and tang adv nonlinear anal 9 496 515 2020 and some new tricks we prove that the nonlinear problem of kirchhoff type a b r3 u 2dx u v x u f u x r3 in h1 r3 admits two classes of ground state solutions under the general berestycki lions assumptions on the nonlinearity f which are almost necessary conditions as well as some weak assumptions on the potential v moreover we also give a simple minimax characterization of the ground state energy our results improve and extend recent theorems in several directions

a critical kirchhoff type problem involving a nonlocal operator abstract in this paper we show the existence of non negative solutions for a kirchhoff type problem driven by a nonlocal integrodifferential operator that is m u z 2 l k u f x u u 2 2 u in u 0 in r n where l k is an integrodifferential operator with kernel k is a bounded subset of r n m and f are continuous functions z is a functional norm and 2 is a fractional sobolev exponent

kirchhoff type system with linear weak damping and logarithmic nonlinearities abstract for the nonlinear kirchhoff type wave system with logarithmic nonlinearities and weak dissipation the global well posedness of initial boundary value problem is analyzed focusing on the interplay between kirchhoff terms and logarithmic sources we investigate the kirchhoff system controlled by logarithmic forces thus amplifying the difficulties in blow up analysis which is the primary scenario of interest by employing potential well method and concavity method we obtain several results related to the sufficient conditions posed on subcritical initial energy and critical initial energy which is used to classify initial data for global existence and finite time blow up finally via careful analysis involving the unstable invariant set under supercritical initial energy we are able to show an affirmative result that the solution blows up in finite time when initial data satisfy some suitable assumptions

infinitely many solutions for fractional kirchhoff schrodinger poisson systems in this paper we study the existence of infinitely many solutions for a fractional kirchhoff schrodinger poisson system based on variational methods especially the fountain theorem for the subcritical case and the symmetric mountain pass theorem established by kajikiya for the critical case we obtain infinitely many solutions for the system under certain assumptions the novelties of this article lie in the appearance of the possibly degenerate kirchhoff function and weak assumptions on the nonlinear term which are quite mild in this paper we study the existence of infinitely many solutions for a fractional kirchhoff schrodinger poisson system based on variational methods especially the fountain theorem for the subcritical case and the symmetric mountain pass theorem established by kajikiya for the critical case we obtain infinitely many solutions for the system under certain assumptions the novelties of this article lie in the appearance of the possibly degenerate kirchhoff function and weak assumptions on the nonlinear term which are quite mild

regularity of the obstacle problem for a fractional power of the laplace operator given a function and s 0 1 we will study the solutions of the following obstacle problem u in r n s u 0i nr n s u x 0 for those x such that u x x lim x u x 0 we show that when is c 1 s or smoother the solution u is in the space c 1 for every s in the case where the contact set u is convex we prove the optimal regularity result u c 1 s when is only c 1 for a s we prove that our solution u is c 1 for every c 2006 wiley periodicals inc

a finite element method with discontinuous rotations for the mindlin reissner plate model we present a continuous discontinuous finite element method for the mindlin reissner plate model based on continuous polynomials of degree k 2 for the transverse displacements and discontinuous polynomials of degree k 1 for the rotations we prove a priori convergence estimates uniformly in the thickness of the plate and thus show that locking is avoided we also derive a posteriori error estimates based on duality together with corresponding adaptive procedures for controlling linear functionals of the error finally we present some numerical results

numerical approximation of mindlin reissner plates we consider a finite element approximation of the so called mindlin reissner formulation for moderately thick elastic plates we show that stability and optimal error bounds hold independently of the value of the thickness 1 introduction the so called mindlin reissner model for moderately thin plates is often used by engineers in connection with plate and shell problems it is well known that many numerical schemes for this model are satisfactory only when the thickness parameter t is not too small for a very small t some bad behavior such as the locking phenomenon might occur here we present a method which is uniformly good as t goes to zero and we prove optimal error estimates for transversal displacement rotations and shear stresses with constants independent of t

the problem of membrane locking in finite element analysis of cylindrical shells we analyse the problem of membrane locking in h p finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution we show that in the standard finite element method locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder a general strategy of avoiding locking by using modified bilinear forms is introduced and a special implementation of this strategy on aligned rectangular grids is considered

analysis of some low order finite element schemes for mindlin reissner and kirchhoff plates we set up a framework for analyzing mixed finite element methods for the plate problem using a mesh dependent energy norm which applies both to the kirchhoff and to the mindlin reissner formulation of the problem the analysis techniques are applied to some low order finite element schemes where three degrees of freedom are associated to each vertex of a triangulation of the domain the schemes proceed from the mindlin reissner formulation with modified shear energy

stabilized finite element formulations for shells in a bending dominated state we consider the design of finite element methods for the naghdi shell model in the case when the deformation is bending dominated two formulations based on stabilizing techniques are introduced and it is proved that they are stable hence free from locking the theoretical estimates are confirmed by numerical benchmark studies

analysis of a discontinuous galerkin method for the bending problem of koiter shell we present an analysis for a mixed finite element method for the bending problem of koiter shell we derive an error estimate showing that when the geometrical coefficients of the shell mid surface satisfy certain conditions the finite element method has the optimal order of accuracy which is uniform with respect to the shell thickness generally the error estimate shows how the accuracy is affected by the shell geometry and thickness it suggests that to achieve the optimal rate of convergence the triangulation should be properly refined in regions where the shell geometry changes dramatically the analysis is carried out for a balanced method in which the normal component of displacement is approximated by discontinuous piecewise cubic polynomials while the tangential components are approximated by discontinuous piecewise quadratic polynomials with some enrichments on elements affixed to the shell free boundary components of the membrane stress are approximated by continuous piecewise linear functions we also include a theory of balanced higher order elements and a theory of a simpler lower order method

iterative solution methods for plate bending problems multigrid and preconditioned cg algorithm the numerical solution of the linear equations arising from a discretization of the plate bending problem based on the zienkiewicz triangle is studied the finite element scheme proceeds from the mindlin reissner formulation with modified shear energy however the kirchhoff condition is imposed on discrete points a multigrid algorithm is analyzed and numerical examples are provided furthermore a suitable preconditioning is established for the use of conjugate gradients

a note on kirchhoff type equations with hartree type nonlinearities abstract we consider the following kirchhoff type equation in r 3 a b r 3 u 2 d x u 1 g x u 1 x u p u p 2 u where a 0 b 0 are constants 0 3 p 2 6 0 is a parameter and g x is a nonnegative continuous potential satisfying some conditions by using the nehari manifold and the concentration compactness principle we establish the existence of ground state solutions for the equation if the parameter is large enough moreover some concentration behaviors of these solutions as are discussed

a mixed finite element for shell model with free edge boundary conditions part 1 the mixed variational formulation abstract after a very brief recall on general shell theory we construct a mixed variational formulation based on the introduction of a new unknown the rotation of the normal to the medium surface in koiter shell theory for instance this rotation can be expressed with respect to the three components of the displacement field of the medium surface and their derivatives the lagrange multiplier corresponding to this relation known as the kirchhoff love kinematical assumption is also introduced as an independent unknown there are two main difficulties one is due to the differential geometry of surfaces and is rather technical the other is to define correctly the dual space for the kirchhoff love relation the difficulty is similar to the one met in the characterization of the dual space of the sobolev space h 1 being the medium surface of the shell for which a boundary component appears except for clamped shells which is a very restrictive situation

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem

group oriented setting s multisigncryption scheme with threshold designcryption signcryption supports the authenticity and confidently in a single logic step and it has more efficient cost than the signature then encryption approach currently signcryption schemes only support a peer to peer secure message transfer between single users and thus it cannot be adapted to the group users in multiple senders and receivers in this paper we propose a group oriented multisigncryption scheme with threshold designcryption in multi users setting which combines the threshold secret sharing technology zero knowledge proof for the bilinear map equality of two discrete logarithms multi signature and identity based signcryption schemes the ciphertext in the proposed scheme is computed by all the m members in sender group and it can be decrypted only by t out of n members in receiver group we prove the security of the proposed scheme in several models including semantic security unforgeability public ciphertext authenticity and verifiability