on semilinear elliptic equations involving concave convex nonlinearities and sign changing weight function abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with a sign changing weight function with the help of the nehari manifold we prove that there are at least two positive solutions for eq e f in bounded domains

a multiplicity result for the jumping nonlinearity problem abstract we consider a class of nonlinear problems of the form au g x u f where a is an unbounded self adjoint operator on a hilbert space h of l 2 functions r n an arbitrary domain and g r r is a jumping nonlinearity in the sense that the limits lim s g x s s a lim s g x s s b exist and jump over the principal eigenvalue of the operator a under rather general conditions on the operator l and for suitable a b we prove some multiplicity results applications are given to the wave equation and elliptic equations in the whole space r n

some comments on fourier analysis uncertainty and modeling investigation of the problem of simultaneously concentrating a function and its fourier transform has led to some interesting special functions that have widespread applications in engineering they provide a means of proving a rigorous version of an engineering folk theorem called the 2wt theorem many generalizations of these ideas seem to possess a similar elegant mathematical structure a brief descriptive review is given of these developments

a semilinear elliptic system involving nonlinear boundary condition and sign changing weight function abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system e involving nonlinear boundary condition and sign changing weight function with the help of the nehari manifold we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

the nehari manifold for systems of nonlinear elliptic equations abstract this paper deals with the existence and multiplicity results of nonlocal positive solutions to the following system p u u p 1 2 u 1 u u 1 v 1 q v v q 2 v 1 u 1 v 1 v together with dirichlet or mixed boundary conditions under some hypotheses on the parameters p p 1 and q more precisely the system considered corresponds to a perturbed eigenvalue equation combined with a second equation having concave and convex nonlinearities the study is based on the extraction of palais smale sequences in the nehari manifold the behaviour of the energy corresponding to these positive solutions with respect to the real parameters and is established

multiplicity of solutions for a class of quasilinear schrdinger systems in rn this paper deals with a class of quasilinear schrdinger systems in rn by exploiting the nehari manifold method and the concentration compactness principle we establish the existence and multiplicity results of ground state solution when the parameter is sufficiently large we also consider the concentration behavior of these solutions as the parameter

the nehari manifold for a semilinear elliptic system involving sign changing weight functions abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system e with sign changing weight function with the help of the nehari manifold we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

a remark on the existence of multiple solutions to a multiparameter nonlinear elliptic system abstract in this work motivated by t f wu the nehari manifold for a semilinear elliptic system involving sign changing weight function nonlinear anal 68 2008 1733 1745 and using recent ideas from brown and wu k j brown t f wu a semilinear elliptic system involving nonlinear boundary condition and sign changing weight function j math anal appl 337 2008 1326 1336 we prove the existence of nontrivial nonnegative solutions to the nonlinear elliptic system p u m x u p 2 u u 2 u c x u 2 u v x p v m x v p 2 v v 2 v c x u v 2 v x u 0 v x here p denotes the p laplacian operator defined by p z div z p 2 z p 2 r n is a bounded domain with smooth boundary 1 1 2 p p p p n n p if n p p if n p n is the outer normal derivative r 2 0 0 the weight m x is a bounded function with m 0 and c x is a continuous function which changes sign in

existence of multiple solutions for quasilinear systems via fibering method existence and multiplicity results for a general class of radial quasilinear equations are proved using the fibering method introduced and developed by s i pohozaev

a new property of reproducing kernels for classical orthogonal polynomials abstract we exhibit a second order differential operator commuting with the reproducing kernel n 0 t n n h n each time that n is one of the classical orthogonal polynomials jacobi laguerre hermite and bessel this is the analog of a known property in the study of time and band limited signals

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

nehari manifold and existence of positive solutions to a class of quasilinear problems abstract in this paper existence and multiplicity results to the following nonlinear elliptic equation p u u q 2 u u p 2 u u 0 in r n together with mixed dirichlet neumann or neumann boundary conditions are established here p u denotes the p laplacian operator 1 q p n p np n p and is a positive real parameter the study is based on the extraction of palais smale sequences in the nehari manifold

existence of multiple positive solutions to singular elliptic systems involving critical exponents abstract this paper is devoted to investigate multiple positive solutions to a singular elliptic system where the nonlinearity involves a combination of concave and convex terms by exploiting the effect of the coefficient of the critical nonlinearity and a variational method we establish the main result which is based on the argument of the compactness

on a system of reaction diffusion equations describing a population with two age groups abstract a system of reaction diffusion equations modelling a population divided into juvenile and adult age groups is studied the system is not co operative but its linear part is and this makes it possible to establish existence non existence and stability results for non negative solutions of the system in terms of the principal eigenvalue of the corresponding linearized system

the nehari manifold for a semilinear elliptic equation with a sign changing weight function abstract the nehari manifold for the equation u x a x u x b x u x 1u x for x together with dirichlet boundary conditions is investigated exploiting the relationship between the nehari manifold and fibrering maps i e maps of the form t j tu where j is the euler functional associated with the equation we discuss how the nehari manifold changes as changes and show how existence and non existence results for positive solutions of the equation are linked to properties of the manifold

existence of three solutions for a class of dirichlet quasilinear elliptic systems involving the p1 pn laplacian abstract in this paper we prove the existence of at least three weak solutions for the quasilinear elliptic systems p 1 u 1 f u 1 x u 1 u 2 u n 0 in p 2 u 2 f u 2 x u 1 u 2 u n 0 in p n u n f u n x u 1 u 2 u n 0 in u i 0 for 1 i n on our main tool is a recent three critical points theorem of ricceri b ricceri on a three critical points theorem arch math basel 75 2000 220 226

determining group structure from the sets of character degrees let cd g be the set of all irreducible complex characters of a finite group g in 4 lewis proved that if p q r and s are distinct primes and cd g 1 p q r pq pr or cd g 1 p q r s pr ps qr qs then g is the direct product of two normal non abelian subgroups of g we generalize lewis results by loosening the primeness hypothesis of cd g

a remark on the uniqueness of positive solutions for some dirichlet problems abstract in this paper we prove the uniqueness of positive weak solutions to the problem p u g x u x u 0 x by a direct argument here is a bounded domain in r n n 3 with smooth boundary p denotes the p laplacian operator defined by p z div z p 2 z p 1 g x 0 0 for a e x and g x u is a caratheodory function we provide a direct uniqueness proof for this problem under certain conditions

toeplitz matrices commuting with tridiagonal matrices abstract we prove that if r is a nonscalar toeplitz matrix ri j r i j which commutes with a tridiagonal matrix with simple spectrum then r k r 1 u k 1 r 2 r 1 cos p u k 1 cos p k 4 5 with uk the chebychev polynomial of the second kind where p is determined from cos p 1 2 r 2 1 r 1 r 3 r 2 2 r 1 r 3

multiple solutions for a class of biharmonic elliptic systems with sobolev critical exponent abstract in this paper we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic systems with sobolev critical exponent in a bounded domain by using the variational method and the nehari manifold we obtain the existence and multiplicity results of nontrivial solutions for the systems

on a nonhomogeneous elliptic system with changing sign data abstract in this paper we give some existence results for multiple positive solutions to the following nonhomogeneous elliptic system s u a u 1 u u 1 v 1 f x in v b v 1 u 1 v v 1 g x in u v 0 on where is a regular bounded domain in r n n 3 0 a b nonnegative reals and are positive parameters and f g are given changing sign functions