on a class of quasilinear schrodinger equations with superlinear or asymptotically linear terms abstract we study the existence and nonexistence of nonzero solutions for the following class of quasilinear schrodinger equations u v x u 2 u 2 u h u x r n where 0 is a parameter v x is a continuous potential which is large at infinity and the nonlinearity h can be asymptotically linear or superlinear at infinity in order to prove our existence result we have applied minimax techniques together with careful l estimates moreover we prove a pohozaev identity which justifies that 2 2 n n 2 is the critical exponent for this class of problems and it is also used to show nonexistence results

local superlinearity and sublinearity for the p laplacian we study the existence nonexistence and multiplicity of positive solutions for a family of problems updelta p u f lambda x u u in w 0 1 p upomega where is a bounded domain in mathbb r n n p and 0 is a parameter the family we consider includes the well known nonlinearities of ambrosetti brezis cerami type in a more general form namely lambda a x u q b x u r where 0 leqslant q p 1 r leqslant p 1 here the coefficient a x is assumed to be nonnegative but b x is allowed to change sign even in the critical case preliminary results of independent interest include the extension to the p laplacian context of the brezis nirenberg result on local minimization in w 0 1 p text and c 0 1 a c 1 alpha estimate for equations of the form updelta p u h x u with h of critical growth a strong comparison result for the p laplacian and a variational approach to the method of upper lower solutions for the p laplacian

holder bounds and regularity of emerging free boundaries for strongly competing schrodinger equations with nontrivial grouping abstract we study interior regularity issues for systems of elliptic equations of the type u i f i x j i a i j u i u i p 1 u j p 1 set in domains r n for n 1 the paper is devoted to the derivation of c 0 estimates that are uniform in the competition parameter 0 as well as to the regularity of the limiting free boundary problem obtained for the main novelty of the problem under consideration resides in the non trivial grouping of the densities in particular we assume that the interaction parameters a i j are only non negative and thus may vanish for specific couples i j as a main consequence in the limit densities do not segregate pairwise in general but are grouped in classes which in turn form a mutually disjoint partition moreover with respect to the literature we consider more general forcing terms sign changing solutions and an arbitrary p 0 in addition we present a regularity theory of the emerging free boundary defined by the interface among different segregated groups these equations are very common in the study of bose einstein condensates and are of key importance for the analysis of optimal partition problems related to high order eigenvalues

multiplicity of solutions for singular quasilinear schrodinger equations with critical exponents abstract by variational methods we study the existence of multiplicity of solutions for singular quasilinear schrodinger equations

the existence and nonexistence of entire large solutions for a quasilinear schrodinger elliptic system by dual approach abstract in this paper we establish some new results on the existence and nonexistence of radial large positive solutions for a modified schrodinger system with a nonconvex diffusion term by a successive iteration technique and the dual approach the necessary and sufficient condition for the existence of radial large positive solutions is established our results improve and extend many previous work in this field of research

uniqueness and non degeneracy of positive radial solutions for quasilinear elliptic equations with exponential nonlinearity abstract we are concerned with the uniqueness and non degeneracy result of positive solutions for a class of quasilinear elliptic equations with exponential nonlinearity we convert a quasilinear elliptic equation into a semilinear one and study precise correspondences between two equations we show the uniqueness and the non degeneracy of positive solutions by analyzing the converted semilinear problem

existence and extendibility of rotationally symmetric graphs with a prescribed higher mean curvature function in euclidean and minkowski spaces abstract in this paper we investigate the existence of rotationally symmetric entire graphs resp entire spacelike graphs with prescribed k th mean curvature function in euclidean space r n 1 resp minkowski spacetime l n 1 as a previous step we analyze the associated homogeneous dirichlet problem on a ball which is not elliptic for k 1 and then we prove that it is possible to extend the solutions moreover a sufficient condition for uniqueness is given in both cases

new stress assumption for hybrid stress elements and refined four node plane and eight node brick elements a new stress assumption for hybrid stress elements is presented generalized incompatible modes are proposed and incorporated into the constraint equations for assumed stresses the physical meaning of the resulting constraint equations is discussed the present stress assumption which can consider the mesh distortion more rigorously is based on the physical interpretation of the role of the generalized incompatible modes and substantiated with simple mesh distortion measures defined in this paper the stress assumption is adapted to the previous four node hybrid stress element 5 i and the eight node hybrid stress brick element 18 which results in a new four node plane element m5 and an new eight node brick element m18 numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion and in high accuracy of stresses 1997 john wiley sons ltd

multiple positive radial solutions for a dirichlet problem involving the mean curvature operator in minkowski space abstract we study the dirichlet problem with mean curvature operator in minkowski space div v 1 v 2 x v q 0 in b r v 0 on b r where 0 is a parameter q 1 r 0 0 r is continuous strictly positive on 0 and b r x r n x r using upper and lower solutions and leray schauder degree type arguments we prove that there exists 0 such that the problem has zero at least one or at least two positive radial solutions according to 0 or moreover is strictly decreasing with respect to r

positive solutions of the dirichlet problem for the prescribed mean curvature equation in minkowski space abstract we prove the existence of multiple positive solutions of the dirichlet problem for the prescribed mean curvature equation in minkowski space div u 1 u 2 f x u u in u 0 on here is a bounded regular domain in r n and the function f f x s is either sublinear or superlinear or sub superlinear near s 0 the proof combines topological and variational methods

positive solutions of the dirichlet problem for the prescribed mean curvature equation abstract we discuss existence and multiplicity of positive solutions of the prescribed mean curvature problem div u 1 u 2 f x u in u 0 on in a general bounded domain r n depending on the behavior at zero or at infinity of f x s or of its potential f x s 0 s f x t d t our main effort here is to describe in a way as exhaustive as possible all configurations of the limits of f x s s 2 at zero and of f x s s at infinity which yield the existence of one two three or infinitely many positive solutions either strong or weak or bounded variation solutions are considered our approach is variational and combines critical point theory the lower and upper solutions method and elliptic regularization

on the speed rate of convergence of solutions to conservation laws with nonlinear diffusions abstract in this paper we analyze the long time behavior of solutions to conservation laws with nonlinear diffusion terms of different types saturating diffusions monotone and non monotone and singular nonlinear diffusions are considered in particular the cases of mean curvature type diffusions both in the euclidean space and in lorentz minkowski space enter in our framework after dealing with existence and stability of monotone steady states in a bounded interval of the real line with dirichlet boundary conditions we discuss the speed rate of convergence to the asymptotic limit as t finally in the particular case of a burgers flux function we show that the solutions exhibit the phenomenon of metastability

variational approach to mems model with fringing field abstract we study semilinear elliptic equations which are called mems model with fringing field using the variational method and dual approach we show the multiple existence of positive solutions

a robust refined quadrilateral plane element based on a rational choice of the internal incompatible displacement function and a special formulation of the a priori elimination of the internal non conforming displacement parameters a new refined quadrilateral plane element rq4 has been developed the present element can be shown to be computationally efficient accurate and free from locking and is better than other elements such as the plan s element hs the generalized hybrid element qcs6 and the refined hybrid element rgh4 etc several numerical examples are given to show the superior performances of the present element rq4

analytic trapezoidal fourier p element for vibrating plane problems a trapezoidal fourier p element for the in plane vibration analysis of two dimensional elastic solids is presented trigonometric functions are used as enriching functions instead of polynomials to avoid ill conditioning problems the element matrices are analytically integrated in closed form with the additional fourier degrees of freedom d o f s the accuracy of the computed natural frequencies is greatly increased one element can predict many modes accurately since a triangle can be divided into three trapezoidal elements the range of application is much wider than the previously derived rectangular fourier p element numerical examples show that convergence is very fast with respect to the number of trigonometric terms comparison of natural modes calculated by the trapezoidal fourier p element and the conventional finite elements is carried out the results show that the trapezoidal fourier p element produces much higher accurate modes than the conventional finite elements with the same number of d o f s for a benchmark problem the condition number of the mass matrix using legendre p element increases rapidly and it becomes non positive with 22 terms the condition numbers of the fourier p element matrices are consistently much lower than those of the legendre p element

le nombre de solutions de certains problemes semi lineaires elliptiques abstract in this paper we compute the exact number of solutions for certain semi linear elliptic problems in the first part we derive some complementary results to a theorem of ambrosetti and prodi the global behaviour of bifurcating branches is then studied for some classes of problems in the context of a concave or a convex nonlinearity in the second part we consider the branch of positive solutions lastly in the third part in dimension one for an autonomous equation we obtain a precise description of all the solutions to these problems the proofs rely on simple eigenvalue comparison arguments

modifying the bfgs update by a new column scaling technique letb be a positive definite symmetric approximation to the second derivative matrix of the objective function of a minimization calculation we study modifications of the bfgs method that apply a scaling technique to the columns of a conjugate direction matrixz satisfyingz t bz i for a simple scaling technique similar to the ones considered by powell 1987 and 1989 we show that due to a two iteration cycle linear convergence can occur when the method is applied to a quadratic function and wolfe s line search is employed although for exact line searches quadratic termination can be proved we then suggest a different scaling technique that prevents certain columns thought to contain important curvature information from being scaled for this algorithm we prove global and superlinear convergence and demonstrate the superiority of our method over the bfgs formula on a range of illconditioned optimization problems moreover we present an implementation of our algorithm that requires only 3n 2 o n multiplications per iteration

nonconstant positive radial solutions for neumann problem involving the mean extrinsic curvature operator abstract let b be the unit ball in r n with n 2 let f c 1 0 r f 0 0 f for some 0 f s s for s 0 f s s for s and f k r where k r is the k th radial eigenvalue of i in the unit ball with neumann boundary condition we use the unilateral global bifurcation theorem to show the existence of nonconstant positive radial solutions of the quasilinear neumann problem div u 1 u 2 u f u in b u 0 on b

classical and non classical solutions of a prescribed curvature equation we discuss existence and multiplicity of positive solutions of the one dimensional prescribed curvature problem u root 1 u 2 lambda f t u u 0 0 u 1 0 depending on the behaviour at the origin and at infinity of the potential integral u 0 f t s ds besides solutions in w 2 w 1 0 1 we also consider solutions in w loc 2 1 0 1 which are possibly discontinuous at the endpoints of 0 1 our approach is essentially variational and is based on a regularization of the action functional associated with the curvature problem c 2007 elsevier inc all rights reserved

multiple solutions of semilinear elliptic problems in a ball in this paper lower bounds for the number of solutions of semilinear elliptic problems in a ball of rn are given its hypotheses are only related to the behavior of the nonlinearities at and at 0 global assumptions are never made for example oddness is never required for the proof of multiplicity results

positive rotationally symmetric solutions for a dirichlet problem involving the higher mean curvature operator in minkowski space abstract in this paper we investigate the global behavior of positive rotationally symmetric solutions for dirichlet problem involving the k th mean curvature operator in minkowski space l n 1 which is not elliptic for k 1 the proofs of our main results are based upon bifurcation techniques

mountain pass solutions for non local elliptic operators abstract the purpose of this paper is to study the existence of solutions for equations driven by a non local integrodifferential operator with homogeneous dirichlet boundary conditions these equations have a variational structure and we find a non trivial solution for them using the mountain pass theorem to make the nonlinear methods work some careful analysis of the fractional spaces involved is necessary we prove this result for a general integrodifferential operator of fractional type and as a particular case we derive an existence theorem for the fractional laplacian finding non trivial solutions of the equation s u f x u in u 0 in r n as far as we know all these results are new

solutions for a class of quasilinear schrodinger equations with critical sobolev exponents in this paper we study a class of quasilinear schrodinger equations involving a critical exponent which arises in plasma physics by using the change of variable and variational approaches combining the concentration compactness principle the existence of a positive solution which has a local maximum point and decays exponentially is obtained

a double parameter scaled bfgs method for unconstrained optimization abstract a double parameter scaled bfgs method for unconstrained optimization is presented in this method the first two terms of the known bfgs update formula are scaled with a positive parameter while the third one is scaled with another positive parameter these parameters are selected in such a way as to improve the eigenvalues structure of the bfgs update the parameter scaling the first two terms of the bfgs update is determined by clustering the eigenvalues of the scaled bfgs matrix on the other hand the parameter scaling the third term is determined as a preconditioner to the hessian of the minimizing function combined with the minimization of the conjugacy condition from conjugate gradient methods under the inexact wolfe line search the global convergence of the double parameter scaled bfgs method is proved in very general conditions without assuming the convexity of the minimizing function using 80 unconstrained optimization test functions with a medium number of variables the preliminary numerical experiments show that this double parameter scaled bfgs method is more efficient than the standard bfgs update or than some other scaled bfgs methods

anisotropic elliptic problems involving hardy type potentials abstract in this paper we give existence uniqueness and regularity of the solutions of problems whose prototype is h u h o x 2 u f x in u 0 on where is a bounded open set of r n n 2 and 0 here h is a norm on r n h o is its polar and h u div h d u h d u is the anisotropic laplacian

least energy solitary waves for a system of nonlinear schrodinger equations in mathbb r n in this paper we consider systems of coupled schrodinger equations which appear in nonlinear optics the problem has been considered mostly in the one dimensional case here we make a rigorous study of the existence of least energy standing waves solitons in higher dimensions we give conditions on the parameters of the system under which it possesses a solution with least energy among all multi component solutions conditions under which the system does not have positive solutions and the associated energy functional cannot be minimized on the natural set where the solutions lie

nonexistence and optimal decay of supersolutions to choquard equations in exterior domains we consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the riesz potential of a power this family of equations includes the choquard or nonlinear schrodinger newton equation we show that for some values of the parameters the equation does not have nontrivial nonnegative supersolutions in exterior domains the same techniques yield optimal decay rates when supersolutions exist 2013 elsevier inc

the p laplacian with respect to measures abstract we introduce a definition for the p laplace operator with respect to positive and finite borel measures that satisfy an adams type embedding condition

a class of quasilinear schrodinger equations with critical or supercritical exponents abstract we study the existence of nontrivial solutions for the following quasilinear schrodinger equations u v x u 2 u 2 u l u x r n where v r n r and l u involves critical or supercritical exponents

pairs of positive radial solutions for a minkowski curvature neumann problem with indefinite weight abstract we prove the existence of a pair of positive radial solutions for the neumann boundary value problem div u 1 u 2 a x u p 0 in b u 0 on b where b is a ball centered at the origin a x is a radial sign changing function with b a x d x 0 p 1 and 0 is a large parameter the proof is based on the leray schauder degree theory and extends to a larger class of nonlinearities

thomas fermi approximation for coexisting two component bose einstein condensates and nonexistence of vortices for small rotation we study minimizers of a gross pitaevskii energy describing a two component bose einstein condensate confined in a radially symmetric harmonic trap and set into rotation we consider the case of coexistence of the components in the thomas fermi regime where a small parameter varepsilon conveys a singular perturbation the minimizer of the energy without rotation is determined as the positive solution of a system of coupled pdes for which we show uniqueness the limiting problem for varepsilon 0 has degenerate and irregular behavior at specific radii where the gradient blows up by means of a perturbation argument we obtain precise estimates for the convergence of the minimizer to this limiting profile as varepsilon tends to 0 for low rotation based on these estimates we can show that the ground states remain real valued and do not have vortices even in the region of small density

the revised dfp algorithm without exact line search in this paper we discuss the convergence of the dfp algorithm with revised search direction under some inexact line searches we prove that the algorithm is globally convergent for continuously differentiable functions and the rate of convergence of the algorithm is one step superlinear and n step second order for uniformly convex objective functions from the proof of this paper we obtain the superlinear and n step second order convergence of the dfp algorithm for uniformly convex objective functions

on the electrostatic born infeld equation with extended charges in this paper we deal with the electrostatic born infeld equation left begin array ll operatorname div left displaystyle frac nabla phi sqrt 1 nabla phi 2 right rho quad in mathbb r n displaystyle lim x to infty phi x 0 end array right quad quad quad quad mathcal bi where rho is an assigned extended charge density we are interested in the existence and uniqueness of the potential phi and finiteness of the energy of the electrostatic field nabla phi we first relax the problem and treat it with the direct method of the calculus of variations for a broad class of charge densities assuming rho is radially distributed we recover the weak formulation of mathcal bi and the regularity of the solution of the poisson equation under the same smoothness assumptions in the case of a locally bounded charge we also recover the weak formulation without assuming any symmetry the solution is even classical if rho is smooth then we analyze the case where the density rho is a superposition of point charges and discuss the results in kiessling commun math phys 314 509 523 2012 other models are discussed as for instance a system arising from the coupling of the nonlinear klein gordon equation with the born infeld theory

reduced hessian quasi newton methods for unconstrained optimization quasi newton methods are reliable and efficient on a wide range of problems but they can require many iterations if the problem is ill conditioned or if a poor initial estimate of the hessian is used in this paper we discuss methods designed to be more efficient in these situations all the methods to be considered exploit the fact that quasi newton methods accumulate approximate second derivative information in a sequence of expanding subspaces associated with each of these subspaces is a certain reduced approximate hessian that provides a complete but compact representation of the second derivative information approximated up to that point algorithms that compute an explicit reduced hessian approximation have two important advantages over conventional quasi newton methods first the amount of computation for each iteration is significantly less during the early stages this advantage is increased by forcing the iterates to linger on a manifold whose dimension can be significantly smaller than the subspace in which curvature has been accumulated second approximate curvature along directions that lie off the manifold can be reinitialized as the iterations proceed thereby reducing the influence of a poor initial estimate of the hessian these advantages are illustrated by extensive numerical results from problems in the cute test set our experiments provide strong evidence that reduced hessian quasi newton methods are more efficient and robust than conventional bfgs methods and some recently proposed extensions

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

positive periodic solutions to an indefinite minkowski curvature equation abstract we investigate the existence non existence multiplicity of positive periodic solutions both harmonic i e t periodic and subharmonic i e kt periodic for some integer k 2 to the equation u 1 u 2 a t g u 0 where 0 is a parameter a t is a t periodic sign changing weight function and g 0 0 is a continuous function having superlinear growth at zero in particular we prove that for both g u u p with p 1 and g u u p 1 u p q with 0 q 1 p the equation has no positive t periodic solutions for close to zero and two positive t periodic solutions a small one and a large one for large enough moreover in both cases the small t periodic solution is surrounded by a family of positive subharmonic solutions with arbitrarily large minimal period the proof of the existence of t periodic solutions relies on a recent extension of mawhin s coincidence degree theory for locally compact operators in product of banach spaces while subharmonic solutions are found by an application of the poincare birkhoff fixed point theorem after a careful asymptotic analysis of the t periodic solutions for

a complete classification of bifurcation diagrams for a class of p q laplace equations abstract we study the bifurcation problem of positive solutions for the one dimensional p q laplace equation with nonlinear term u r 1 there are five types of order relations for p q r we investigate the exact shape of the bifurcation curve in each type of the order relation we prove that there are two types of bifurcation curves that are increasing two types that are decreasing and one that is not monotone and turns exactly once moreover we study the asymptotic profile of the normalized solution u x u as u 0 or u where u denotes the l norm of u

existence of ground state solutions for a quasilinear schrodinger equation with critical growth we establish the existence of ground state solutions for a quasilinear schrodinger equation u v x u u 2 u u 2 2 2 u u p 1 u in r n where n 3 2 2 n n 2 1 p 2 2 1 and 0 is a parameter we do not need the subcritical exponent p 3 which was used by several authors to conclude the existence of solution for the equation above

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

c1 α local regularity of weak solutions of degenerate elliptic equations abstract it is demonstrated the local c 1 alpha nature of weak solutions of elliptic equations of the type 1 1 in the introduction under the degeneracy or singularity assumptions a sub 1 a sub 3

new existence and symmetry results for least energy positive solutions of schrodinger systems with mixed competition and cooperation terms abstract in this paper we focus on existence and symmetry properties of solutions to the cubic schrodinger system u i i u i j 1 d i j u j 2 u i in r n i 1 d where d 2 i i i 0 i j j i r for j i n 2 3 the underlying domain is either bounded or the whole space and u i h 0 1 or u i h rad 1 r n respectively we establish new existence and symmetry results for least energy positive solutions in the case of mixed cooperation and competition coefficients as well as in the purely cooperative case

symmetry properties of positive solutions for fully nonlinear elliptic systems abstract we investigate symmetry properties of positive solutions for fully nonlinear uniformly elliptic systems such as f i x d u i d 2 u i f i x u 1 u n d u i 0 1 i n in a bounded domain in r n with dirichlet boundary condition u 1 u n 0 on here f i s are nonincreasing with the radius r x and satisfy a cooperativity assumption in addition each f i is the sum of a locally lipschitz with a nondecreasing function in the variable u i and may have superlinear gradient growth we show that symmetry occurs for systems with nondifferentiable f i s by developing a unified treatment of the classical moving planes method in the spirit of gidas ni nirenberg we also present different applications of our results including uniqueness of positive solutions for lane emden systems in the subcritical case in a ball and symmetry for a class of systems with natural growth in the gradient

nonlinear schrodinger equation in the bopp podolsky electrodynamics solutions in the electrostatic case abstract we study the following nonlinear schrodinger bopp podolsky system u u q 2 u u p 2 u a 2 2 4 u 2 in r 3 with a 0 we prove existence and nonexistence results depending on the parameters q p moreover we also show that in the radial case the solutions we find tend to solutions of the classical schrodinger poisson system as a 0

the thomas fermi von weizsacker theory of atoms and molecules we place the thomas fermi von weizsacker model of atoms on a firm mathematical footing we prove existence and uniqueness of solutions of the thomas fermi von weizsacker equation as well as the fact that they minimize the thomas fermi von weizsacker energy functional moreover we prove the existence of binding for two very dissimilar atoms in the frame of this model

automatic column scaling strategies for quasi newton methods a class of algorithms is described for unconstrained optimization based on the bfgs update formula which includes an automatic column scaling strategy the new algorithms generalize the method of powell math programming 38 1987 pp 29 46 conditions are given on the scaling strategies that guarantee global and superlinear convergence on convex problems

coupled klein gordon and born infeld type equations looking for solitary waves the existence of infinitely many non trivial radially symmetric solitary waves for the nonlinear klein gordon equation coupled with a born infeld type equation is established under general assumptions

uniqueness of positive solutions of δu f u 0 in ℝn n 3 we study the uniqueness of radial ground states for the semilinear elliptic partial differential equation delta u f u 0 eqno in n we assume that the function f has two zeros the origin and u 0 0 above u 0 the function f is positive is locally lipschitz continuous and satisfies convexity and growth conditions of a superlinear nature below u 0 f is assumed to be non positive non identically zero and merely continuous our results are obtained through a careful analysis of the solutions of an associated initial value problem and the use of a monotone separation theorem it is known that for a large class of functions f the ground states of are radially symmetric in these cases our result implies that possesses at most one ground state

asymmetric poincare inequalities and solvability of capillarity problems abstract in this paper we first establish an asymmetric version of the poincare inequality in the space of bounded variation functions and then basically relying on this result we discuss the existence the non existence and the multiplicity of bounded variation solutions of a class of capillarity problems with asymmetric perturbations

positive solutions to classes of infinite semipositone p q laplace problems with nonlinear boundary conditions abstract we consider one dimensional p q laplace problems u h t f u t 0 1 u 0 0 a u 1 g u 1 u 1 where 0 a 0 s s p 2 s s q 2 s 1 p q h c 0 1 0 f c 0 r with lim s 0 f s 0 and g c 0 0 0 such that g r s s is nondecreasing with respect to s 0 classifying the behaviors of f near infinity we establish the existence multiplicity and nonexistence of positive solutions in particular we provide a sufficient condition on f to obtain a multiplicity result for the case when lim s f s s r 1 0 1 r q which is new even in semilinear problems p q 2 the proofs are based on a krasnoselskii type fixed point theorem which is fit to overcome a lack of homogeneity

asymptotic uniqueness of ground states for a class of quasilinear schrodinger equations with h 1 supercritical exponent in this paper we obtain the asymptotic uniqueness of ground states for a class of quasilinear schrodinger equations with h1 supercritical exponent to this aim the uniqueness and the non degeneracy of positive solutions of the corresponding limit equation which is a zero mass problem play important roles thus we also show the uniqueness and non degeneracy result for a class of zero mass problems by applying ode techniques

analysis of a self scaling quasi newton method we study the self scaling bfgs method of oren and luenberger 1974 for solving unconstrained optimization problems for general convex functions we prove that the method is globally convergent with inexact line searches we also show that the directions generated by the self scaling bfgs method approach newton s direction asymptotically this would ensure superlinear convergence if in addition the search directions were well scaled but we show that this is not always the case we find that the method has a major drawback to achieve superlinear convergence it may be necessary to evaluate the function twice per iteration even very near the solution an example is constructed to show that the step sizes required to achieve a superlinear rate converge to 2 and 0 5 alternately

a ground state solution for an asymptotically periodic quasilinear schrodinger equation abstract this article is concerned with the existence of positive ground state solutions for an asymptotically periodic quasilinear schrodinger equation by using a change of variables the quasilinear problem is transformed into a semilinear one then we use a nehari type constraint to get the existence result

multiple solutions to a class of generalized quasilinear schrodinger equations with a kirchhoff type perturbation abstract in this paper we consider a class of generalized quasilinear schrodinger equations with a kirchhoff type perturbation under the assumption that the potential may be vanishing at infinity the existence of both the ground state and the ground state sign changing solutions is established furthermore the behavior of these solutions is studied when the perturbation vanishes it is a surprise that we find an interesting phenomenon about the monotonicity for the quotient function as a byproduct

multiple normalized solutions for quasi linear schrodinger equations abstract in this paper we prove the existence of two solutions having a prescribed l 2 norm for a quasi linear schrodinger equation one of these solutions is a mountain pass solution relative to a constraint and the other one a minimum either local or global to overcome the lack of differentiability of the associated functional we rely on a perturbation method developed in 25

existence results for the p laplacian with nonlinear boundary conditions in this paper we study the existence of nontrivial solutions for the problem pu u p 2u in a bounded smooth domain rn with a nonlinear boundary condition given by u p 2 u f u on the boundary of the domain the proofs are based on variational and topological arguments

blow up phenomena and asymptotic profiles of ground states of quasilinear elliptic equations with h1 supercritical nonlinearities abstract this paper is concerned with asymptotic profiles of ground states for a class of quasilinear schrodinger equations with h 1 supercritical nonlinearities we study the blow up rate of ground states by using the dual variational structure of equations as well as various variational methods

multiple solutions for quasilinear schrodinger equations with a parameter abstract in this paper we study the following quasilinear schrodinger equations of the form u v x u u 2 u 2 2 u g x u x r n where 1 1 2 v c r n r g c r n r r using some special techniques the existence of positive solutions negative solutions and sequence of high energy solutions are studied

spacelike hypersurfaces with prescribed boundary values and mean curvature we consider the boundary value problem for the mean curvature operator in minkowski space and give necessary and sufficient conditions for the existence of smooth strictly spacelike solutions our main results hold for non constant mean curvature and make no assumptions about the smoothness of the boundary or boundary data

positive radial solutions for dirichlet problems with mean curvature operators in minkowski space abstract in this paper by using leray schauder degree arguments and critical point theory for convex lower semicontinuous perturbations of c 1 functionals we obtain existence of classical positive radial solutions for dirichlet problems of type div v 1 v 2 f x v 0 in b r v 0 on b r here b r x r n x r and f 0 r 0 r is a continuous function which is positive on 0 r 0

on the structure of fractional degree vortices in a spinor ginzburg landau model abstract we consider a ginzburg landau functional for a complex vector order parameter whose minimizers exhibit vortices with half integer degree by studying the associated system of equations in r 2 which describes the local structure of these vortices we show some new and unconventional properties of these vortices in particular one component of the solution vanishes but the other does not we also prove the existence and uniqueness of equivariant entire solutions and provide a second proof of uniqueness valid for a large class of systems with variational structure

local superlinearity and sublinearity for indefinite semilinear elliptic problems in this paper the usual notions of superlinearity and sublinearity for semilinear problems like du f x u are given a local form and extended to indefinite nonlinearities here f x s is allowed to change sign or to vanish for s near zero as well as for s near infinity some of the well known results of ambrosetti bre zis cerami are partially extended to this context

positive radial solutions for multiparameter dirichlet systems with mean curvature operator in minkowski space and lane emden type nonlinearities abstract we deal with dirichlet systems involving the mean curvature operator in minkowski space m w div w 1 w 2 in a ball in r n using the fixed point index and the lower and upper solutions method we first obtain the existence of positive solutions for a class of differential systems with a singular laplacian subjected to homogeneous mixed boundary conditions the main application of the general results concerns dirichlet systems with lane emden type nonlinearities in a superlinear case depending on two parameters 1 2 so we prove that for such a system there exists a continuous curve which separates the first quadrant in two disjoint unbounded open sets o 1 and o 2 such that the system has zero at least one or at least two radial positive solutions according to 1 2 o 1 1 2 or 1 2 o 2

three dimensional 8 node and 20 node refined hybrid isoparametric elements in this paper a new hybrid variational principle with independent variables of strain stress and displacement and with a weaker constraint condition of interelement continuity is proposed based on this functional a general formulation of a refined hybrid isoparametric element method has been established by the orthogonal approach the present formulation is a rational approach to be adopted for deriving high performance three dimensional hybrid isoparametric elements even up to the higher order 20 node element several numerical examples are presented to show that the present elements rgh8 8 node and rgh20 20 node have high accuracy excellent computational efficiency and less sensitivity to mesh distortion

uniqueness of the ground state solutions of quasilinear schrodinger equations abstract we are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics we convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity we also investigate the non degeneracy of a positive radial solution for a converted semilinear elliptic equation

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

a unified analysis for stress strain hybrid methods of high performance abstract several methods have been developed in the literatures of computational mechanics to improve the performance of the conventional lower order displacement finite elements which yield poor results for problems with bending and for nearly incompressible medium this paper is devoted to a unified analysis of convergence for pian sumihara s chen cheung s and piltner taylor s enhanced stress strain schemes by virtue of the energy compatibility and the rank condition error estimates for these typical finite elements of high performance are obtained in a unified framework and especially weakly locking free error estimates with respect to the poisson s ratio in energy norms are obtained uniformly for 1 ch 2 as h 0 where c is a constant independent of and the mesh size h very much the same about the three methods is pointed out

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

coexistence theorems of steady states for predator prey interacting systems on donne des conditions necessaires et suffisantes pour l existence des solutions positives des etats stationnaires pour des systemes predateur proie sous des conditions aux limites de dirichlet sur r n

ground state solution for a problem with mean curvature operator in minkowski space abstract in this paper we prove the existence of a radial ground state solution for a quasilinear problem involving the mean curvature operator in minkowski space

propagation and blocking in periodically hostile environments we study the persistence and propagation or blocking phenomena for a species in periodically hostile environments the problem is described by a reaction diffusion equation with the zero dirichlet boundary condition we first derive the existence of a minimal nonnegative nontrivial stationary solution and study the large time behavior of the solution of the initial boundary value problem in addition to the main goal we then study a sequence of approximated problems in the whole space with reaction terms with very negative growth rates which are outside the domain under investigation finally for a given unit vector by using the information of the minimal speeds of approximated problems we provide a simple geometric condition for the blocking of propagation and we derive the asymptotic behavior of the approximated pulsating travelling fronts moreover for the case of the constant diffusion matrix we provide two conditions for which the limit of approximated minimal speeds is positive