solitons and the electromagnetic field in a recent paper 4 it has been introduced a lorentz invariant equation in three space dimensions having soliton like solutions we recall that roughly speaking a soliton is a solution whose energy travels as a localized packet and which preserves this form of localization under small perturbations see 6 15 13 10 the equation introduced in 4 is the euler lagrange equation of an action functional

positive solutions for a schrodinger poisson system involving concave convex nonlinearities abstract in this paper we study the critical growth schrodinger poisson system with a concave term and establish the existence of multiple positive solutions via using the variational method

ground state sign changing solutions for a schrodinger poisson system with a 3 linear growth nonlinearity abstract in this paper we investigate the existence and asymptotic behavior of ground state sign changing solutions to a class of schrodinger poisson systems u v x u u f x u u 2 u x r 3 u 2 x r 3 where v is a smooth function f is nonnegative 0 1 and 1 is the first eigenvalue of the problem u v x u f x u in h with the help of the sign changing nehari manifold we obtain that the schrodinger poisson system possesses at least one ground state sign changing solution u for all 0 and each 1 moreover we prove that its energy is strictly larger than twice that of ground state solutions besides we give a convergence property of u as 0 this paper can be regarded as the complementary work of shuai and wang 23 wang and zhou 24

schrodinger poisson equations without ambrosetti rabinowitz condition abstract we prove the existence of ground state solutions for a stationary schrodinger poisson equation in r 3 the proof is based on the mountain pass theorem and it does not require the ambrosetti rabinowitz condition

positive solutions for some non autonomous schrodinger poisson systems abstract in this paper we study the schrodinger poisson system sp u u k x x u a x u p 1 u x r 3 k x u 2 x r 3 with p 3 5 assuming that a r 3 r and k r 3 r are nonnegative functions such that lim x a x a 0 lim x k x 0 and satisfying suitable assumptions but not requiring any symmetry property on them we prove the existence of positive solutions

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

subdivision direction selection in interval methods for global optimization the role of the interval subdivision selection rule is investigated in branch and bound algorithms for global optimization the class of rules that allows convergence for the model algorithm is characterized and it is shown that the four rules investigated satisfy the conditions of convergence a numerical study with a wide spectrum of test problems indicates that there are substantial differences between the rules in terms of the required cpu time the number of function and derivative evaluations and space complexity and two rules can provide substantial improvements in efficiency

positive solutions for schrodinger poisson equations with a critical exponent abstract in this paper we establish the existence of a positive solution of the schrodinger poisson equations with a critical sobolev exponent the methods used here are based on the concentration compactness principle of p l lions and methods of brezis and nirenberg

an interval step control for continuation methods the authors present a step control for continuation methods that is deterministic in the sense that i it computationally but rigorously verifies that the corrector iteration will converge to a point on the same curve as the previous point i e the predictor corrector iteration will never jump across paths and ii each predictor step is as large as possible subject to verification that the curve is unique with the given interval extension the authors present performance data and comparisons with an approximate step control method pitcon version 6 1 a comparison of plots obtained from both step controls reveals that an approximate step control will behave erratically in situations where the interval step control leads to orderly progression along the curve this is true even if the maximum allowable stepsize for the approximate method is set to be smaller than many of the steps actually taken by the interval algorithm limitations of interval step controls are also discussed

preconditioners for the interval gauss seidel method interval newton methods in conjunction with generalized bisection can form the basis of algorithms that find all real roots within a specified box bf x subset bf r n of a system of nonlinear equations f x 0 with mathematical certainty even in finite precision arithmetic in such methods the system f x 0 is transformed into a linear interval system 0 f m bf f bf x bf bar x m if interval arithmetic is then used to bound the solutions of this system the resulting box bf bar x contains all roots of the nonlinear system the interval gauss seidel method is a reasonable way of finding such solution bounds for the overall interval newton bisection algorithm to be efficient the image box bf bar x should be as small as possible to do this the linear interval system is multiplied by a preconditioner matrix y before the interval gauss seidel method is applied in this paper a technique for computing such preconditioner matrices y is described this te

a numerical method for large eddy simulation in complex geometries we discuss the development of a numerical algorithm and solver capable of performing large eddy simulation in the very complex geometries often encountered in industrial applications the algorithm is developed for unstructured hybrid grids is non dissipative yet robust at high reynolds numbers on highly skewed grids simulation results for a variety of flows are presented

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

positive solutions for a schrodinger poisson system with singularity and critical exponent abstract we study multiplicity of positive solutions for a class of schrodinger poisson system with singularity and critical exponent and obtain two positive solutions via the variational and perturbation methods

on ground state solutions for some non autonomous schrodinger poisson systems abstract in this paper we study the schrodinger poisson system sp u u k x x u a x f u in r 3 k x u 2 in r 3 and prove the existence of ground state solutions for system sp under certain assumptions on the linear and nonlinear terms some recent results from different authors are extended

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

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

infinitely many positive solutions for a schrodinger poisson system abstract we are interested in the existence of infinitely many positive solutions of the schrodinger poisson system u u v x u u p 1 u x r 3 v x u 2 x r 3 where v x is a positive bounded function 1 p 5 and v r r x has the following decay property v r a r m o 1 r m with a 0 m 3 2 0 the solutions obtained are non radial

on steplength algorithms for a class of continuation methods the continuation methods considered here are algorithms for the computational analysis of the regular parts of the solution field of equations of the form fx b f d subset r n 1 to r n for given b in r n while these methods are similar in structure to those used for ode solvers their errors are independent of the history of the process and are solely determined by the termination criterion of the corrector at the current step this suggests the use of a posteriors estimates of the convergence radii of the corrector it is proved here that such estimates cannot be obtained from the sequence of corrector iterates alone but that they require some global information about f however it is shown that a finite sequence of corrector iterates does allow for the computation of effective estimates of the convergence quality of certain types of correctors this is used for the design of various step algorithms for continuation processes two of them are based on a newton corrector while the third o

sweeping algebraic curves for singular solutions many problems give rise to polynomial systems these systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters using predictor corrector methods we track the solution paths a point along a solution path is critical when the jacobian matrix is rank deficient the simplest case of quadratic turning points is well understood but these methods no longer work for general types of singularities in order not to miss any singular solutions along a path we propose to monitor the determinant of the jacobian matrix we examine the operation range of deflation and relate the effectiveness of deflation to the winding number computational experiments on systems coming from different application fields are presented

solutions of a schrodinger poisson system with combined nonlinearities abstract in this paper we are concerned with the following schrodinger poisson system u v x u u k x u q 2 u f x u x r 3 u 2 lim x x 0 x r 3 where 0 is a parameter 1 q 2 and f x u is linearly bounded in u at infinity we establish the existence and multiplicity of solutions under suitable assumptions on v k and f

certified parallelotope continuation for one manifolds starting from an initial solution continuation methods efficiently produce a sequence of points on a manifold typically defined as the solution set of an underconstrained system of equations they have a wide range of applications ranging from curve plotting to polynomial root finding by homotopy however classical methods cannot guarantee that the returned points all belong to the same connected component of the manifold i e they may jump from one component to another trying to overcome this issue has given birth to several sophisticated heuristics on the one hand and to guaranteed methods based on rigorous computations on the other hand in this paper we introduce a new rigorous predictor corrector continuation method based on interval computations its novelty lies in the fact that it uses parallelotopes as defined in a goldsztejn and l granvilliers a new framework for sharp and efficient resolution of ncsp with manifolds of solutions constraints 15 2010 pp 190 212 to enclose consecuti

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

multiple solutions for a nonlinear schrodinger poisson system with sign changing potential this paper deals with the existence and multiplicity of nontrivial solutions for a nonlinear schrodinger poisson system under some suitable conditions some criteria on the existence of nontrivial solutions including a ground state solution two solutions and a sequence of nontrivial solutions u k with u k 0 as k is established by applying the morse theory and variational methods some known results in the literatures are extended and improved

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

on ground state solutions for the schrodinger poisson equations with critical growth abstract in this paper we study the existence of ground state solutions for the following schrodinger poisson equation u v x u u u q 1 u u 4 u in r 3 u 2 in r 3 where is a positive parameter under some certain assumptions on v we prove that for every 0 and q 2 5 such a class of schrodinger poisson equation with critical growth has at least a positive ground state solution via variational methods some recent results from the literature are extended

ground state solutions for quasilinear schrodinger equations via pohožaev manifold in orlicz space abstract this paper is concerned with the following quasilinear schrodinger equations u v x u u 2 u u p 1 u in r n u 0 u h 1 r n where 0 1 p 22 1 2 2 n n 2 and n 3 under some suitable assumptions on v x we prove the existence of ground state solutions via poho aev manifold method the novelty of this works with respect to some recent results is that we treat the existence by using poho aev manifold method in an orlicz space and this enables us to handle the nonlinearity in a uniform way as its supplementary results we also prove the nonexistence of least energy solutions for 1 p 22 1

galois groups of schubert problems via homotopy computation numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry whose development has been driven by applications of mathematics we use numerical homotopy continuation to investigate the problem in pure mathematics of determining galois groups in the schubert calculus for example we show by direct computation that the galois group of the schubert problem of 3 planes in 8 meeting 15 fixed 5 planes non trivially is the full symmetric group s 6006

symmetry preserving discretization of turbulent flow we propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators i e the convective operator is represented by a skew symmetric coefficient matrix and the diffusive operator is approximated by a symmetric positive definite matrix mimicking crucial properties of differential operators forms in itself a motivation for discretizing them in a certain manner we give it a concrete form by noting that a symmetry preserving discretization of the navier stokes equations is stable on any grid and conserves the total mass momentum and kinetic energy for the latter the physical dissipation is to be turned off of coarse being stable on any grid the choice of the grid may be based on the required accuracy solely and the main question becomes how accurate is a symmetry preserving discretization its accuracy is tested for a turbulent flow in a channel by comparing the results to those of physical experiments and previous numerical studies the comparison is carried out for a reynolds number of 5600 which is based on the channel width and the mean bulk velocity based on the channel half width and wall shear velocity the reynolds number becomes 180 the comparison shows that with a fourth order symmetry preserving method a 64 64 32 grid suffices to perform an accurate numerical simulation

number and profile of low energy solutions for singularly perturbed klein gordon maxwell systems on a riemannian manifold abstract given a 3 dimensional riemannian manifold m g we investigate the existence of positive solutions of the klein gordon maxwell system e 2 g u a u u p 1 2 q v 1 2 u in m g v 1 q 2 u 2 v q u 2 in m and schrodinger maxwell system e 2 g u u u v u p 1 in m g v v q u 2 in m when p 4 6 we prove that the number of one peak solutions depends on the topological properties of the manifold m by means of the lusternik schnirelmann category

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

adaptive multiprecision path tracking this article treats numerical methods for tracking an implicitly defined path the numerical precision required to successfully track such a path is difficult to predict a priori and indeed it may change dramatically through the course of the path in current practice one must either choose a conservatively large numerical precision at the outset or rerun paths multiple times in successively higher precision until success is achieved to avoid unnecessary computational cost it would be preferable to adaptively adjust the precision as the tracking proceeds in response to the local conditioning of the path we present an algorithm that can be set to either reactively adjust precision in response to step failure or proactively set the precision using error estimates we then test the relative merits of reactive and proactive adaptation on several examples arising as homotopies for solving systems of polynomial equations

multiplicity of small negative energy solutions for a class of nonlinear schrodinger poisson systems this paper deals with the following nonlinear schrodinger poisson email protected v x u k x f x u h x f x u inr 3 email protected f k x u 2 inr 3 where v x k x and h x are nonnegative continuous functions under appropriate assumptions on v x k x h x and f x u we prove the existence of infinitely many small negative energy solutions by using the variant fountain theorem established by zou recent results from the literature are extended

existence and nonexistence of positive solutions for a static schrodinger poisson slater equation abstract in this paper we study the following type of the schrodinger poisson slater equation with critical growth u u 2 1 4 x u u p 1 u u 4 u in r 3 where 0 and p 11 7 5 for the case of p 2 5 we develop a novel perturbation approach together with the well known mountion pass theorem to prove the existence of positive ground states for the case of p 2 we obtain the nonexistence of nontrivial solutions by restricting the range of and also study the existence of positive solutions by the constrained minimization method for the case of p 11 7 2 we use a truncation technique developed by brezis and oswald 9 together with a measure representation concentration compactness principle due to lions 27 to prove the existence of radial symmetrical positive solutions for 0 with some 0 the above results nontrivially extend some theorems on the subcritical case obtained by ianni and ruiz 18 to the critical case

two positive solutions of a class of schrodinger poisson system with indefinite nonlinearity abstract we study the existence and multiplicity of positive solutions of a class of schrodinger poisson system u u l x u k x u p 2 u h x u in r 3 l x u 2 in r 3 where 4 p 6 k c r 3 k changes sign in r 3 and lim x k x k 0 we mainly prove the existence of at least two positive solutions in the case that 1 and near 1 where 1 is the first eigenvalue of i d in h 1 r 3 with weight function h whose corresponding eigenfunction is denoted by e 1 an interesting phenomenon is that we do not need the condition r 3 k x e 1 p d x 0 which has been shown to be a necessary condition to the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearity see e g s alama g tarantello on semilinear elliptic equations with indefinite nonlinearities calc var partial differential equations 1 1993 439 475

mesh stretch effects on convection in flow simulations staggered grids have been widely used with finite difference approaches for incompressible flow simulation they retain conservation properties that stabilize the flow field and avoid odd even decoupling in the pressure field on a non uniform mesh however the accuracy of finite difference schemes is degraded to the order of the mesh stretch if all the conservation properties are to be upheld this study shows how a non uniform numerical mesh creates short wavelength errors in convective terms especially when the grid spacing varies in the streamwise direction the conservation properties of convective schemes on a non uniform mesh can conflict with aspects of numerical accuracy it is crucial to employ an area weighted average for the convection velocity in order to impose mass conservation in the presence of mesh stretching truncation error analysis indicates that energy conserving schemes produce anti diffusion error if the mesh is stretched or positive diffusion if it is narrowed an alternative convection scheme that minimizes the mesh stretch error is proposed and evaluated through numerical simulations the nature of mesh stretch error is illustrated by a direct numerical simulation of turbulent channel flow

existence of ground state solutions for the schrodinger poisson systems abstract in this paper we consider the following schrodinger poisson system e 2 u v x u k x u a x u p 1 u in r 3 e 2 k x u 2 in r 3 with p 1 5 and e 0 we not only investigate the existence of ground state solutions but also employ bifurcation theory to show that the norm of the given ground state solutions tends to zero as the planck constant e 0 moreover we also study some non existence results

multiple positive solutions for a schrodinger newton system with sign changing potential abstract in this paper we study the schrodinger newton systems with sign changing potential in a bounded domain by using the variational method and analytic techniques the existence and multiplicity of positive solutions are established

concentration and compactness in nonlinear schrodinger poisson system with a general nonlinearity in this paper we use a concentration and compactness argument to prove the existence of a nontrivial non radial solution to the nonlinear schrodinger poisson equations in r3 assuming on the nonlinearity the general hypotheses introduced by berestycki and lions

an asymptotically linear schrodinger poisson system on r3 abstract in this paper we are concerned with the following nonlinear schrodinger poisson equation u u u f x u u x r 3 u 2 lim x x 0 where u r 3 r are positive functions the parameters 0 f x s tend to p x and q x l r 3 respectively as s 0 and s under some simple assumptions on f x s we give existence and nonexistence results depending on the parameters and

existence and non existence of solitary waves for the critical klein gordon equation coupled with maxwell s equations abstract in this paper we investigate existence and non existence of solutions for a nonlinear elliptic system arising from the coupling of the nonlinear klein gordon equation with the maxwell equations when the nonlinearity exhibits critical growth we prove a non existence result by a poho aev type argument and then adding a suitable perturbation we recover existence of at least a radially symmetric solution we overcome the lack of compactness relying on the brezis nirenberg method

infinitely many solutions for schrodinger maxwell equations with indefinite sign subquadratic potentials in this paper we deal with multiplicity of solutions of a class of sublinear schrodinger maxwell equations du v x u fu f x u inr 3 d f u 2 lim x f x 0 inr 3 under more relaxed assumptions on v and f we establish some existence criteria to guarantee that the above problem has at least one or infinitely many nontrivial solutions by using the genus properties in critical theory

improving shock free compressible rans solvers for les on unstructured meshes standard numerical methods used to solve the reynolds averaged navier stokes equations are known to be too dissipative to carry out large eddy simulations since the artificial dissipation they introduce to stabilize the discretization of the convection term usually interacts strongly with the subgrid scale model a possible solution is to resort to non dissipative central schemes unfortunately these schemes are in general unstable a way to reach stability is to select a central scheme that conserves the discrete kinetic energy to that purpose a family of kinetic energy conserving schemes is developed to perform simulations of compressible shock free flows on unstructured grids a direct numerical simulation of the flow past a sphere at a reynolds number of 300 and a large eddy simulation at a reynolds number of 10 000 are performed to validate the methodology

a robust and efficient method for solving point distance problems by homotopy the goal of point distance solving problems is to find 2d or 3d placements of points knowing distances between some pairs of points the common guideline is to solve them by a numerical iterative method e g newton raphson method a sole solution is obtained whereas many exist however the number of solutions can be exponential and methods should provide solutions close to a sketch drawn by the user geometric reasoning can help to simplify the underlying system of equations by changing a few equations and triangularizing it this triangularization is a geometric construction of solutions called construction plan we aim at finding several solutions close to the sketch on a one dimensional path defined by a global parameter homotopy using a construction plan some numerical instabilities may be encountered due to specific geometric configurations we address this problem by changing on the fly the construction plan numerical results show that this hybrid method is efficient and robust