Singular quasilinear elliptic problems with indefinite weights and critical potential

The Dirichlet problem for a quasilinear sub-critical inhomogeneous elliptic equation with critical potential and singular coefficients, which has indefinite weights in RN , is studied in this paper. We discuss the corresponding eigenvalue problems by the variational techniques and Picone’s identity, and obtain the existence of non-trivial solutions for the inhomogeneous Dirichlet problem by using Hardy inequality, Mountain Pass Lemma in conjunction with the property of eigenvalues.     

New existence of periodic solutions for second order non-autonomous Hamiltonian systems

By using mountain pass theorem and local link theorem, some existence theorems are obtained for periodic solutions of second order non-autonomous Hamiltonian systems under local superquadratic condition and other suitable conditions.     

Positive solution to a class of relativistic nonlinear Schrödinger equation

Using a change of variables, we convert a quasilinear elliptic equation into a semilinear one. Then by Jeanjean?s result [6], we get a bounded (PS) sequence for the corresponding functional and show the existence of positive nontrivial solution.     

INFINITELY MANY SOLUTIONS TO p（x）-BIHARMONIC PROBLEM WITH NAVIER BOUNDARY CONDITIONS

In this paper, we consider a p（x）-biharmonic problem with Navier boundary conditions. The existence of infinitely many solutions which tend to zero is investigated based on the symmetric Mountain Pass lemma. Our approach relies on the theory of variable exponent Sobolev space.     

Existence of solutions to a class of nonlinear second order two-point boundary value problems

In this paper, the existence and multiplicity results of solutions are obtained for the second order two-point boundary value problem −u^″(t)=f(t,u(t)) for all t∈[0,1] subject to u(0)=u^′(1)=0, where f is continuous. The monotone operator theory and critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator and its properties play an important role.     

HOMOCLINIC ORBITS FOR A CLASS OF HAMILTONIAN SYSTEMS WITH POTENTIALS CHANGING SIGN

In this paper, we prove the existence of nontrivial homoclinic orbits for a class of Hamiltonian systems with potential changing sign. We use Mountain Pass Lemma.     

On the Existence of Positive Solutions for Hemivariational Inequalities Driven by the p-Laplacian

We study nonlinear elliptic problems driven by the p-Laplacian and with a nonsmooth locally Lipschitz potential (hemivariational inequality). We do not assume that the nonsmooth potential satisfies the Ambrosetti--Rabinowitz condition. Using a variational approach based on the nonsmooth critical point theory, we establish the existence of at least one smooth positive solution.Mathematics Subject Classifications (2000). 35J50, 35J85, 35R70.This article is Revised version.Leszek Gasiski is an award holder of the NATO Science FellowshipProgramme, which was spent in the National Technical University of Athens.     

Existence theorems for second-order discrete boundary value problems

This article is concerned with the existence of solutions of boundary value problems for nonlinear second-order difference equations of the type , where δ>0 is the ratio of odd positive integers, {p_n} and {q_n} are real sequences. The authors apply the Linking Theorem and the Mountain Pass Lemma in the critical point theory and give some new results for the existence of solutions.     

一类P—Laplace方程正解的存在性

本文在不满足(AR)条件下,利用山路引理,证明了P-Laplace方程Dirichlet问题正解的存在性.