NONSMOOTH CRITICAL POINT THEOREMS AND ITS APPLICATIONS TO QUASILINEAR SCHRDINGER EQUATIONS

In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.

Three Solutions of p-Laplacian Equations Via a Critical Point Theorem of Ricceri

In this paper,we consider the following quasilinear diferential equation（p（u′））′＋λf（t,u）=0subject to one of the two boundary conditions：u（0）=u′（1）=0,u′（0）=u（1）=0.After transforming them into a problem of symmetrical solutions,the existence of three solutions of the problem is obtained by using a recent critical point theorem of Recceri.An example is given to demonstrate our main result.

Existence of Three Solutions for Quasilinear Elliptic Equations: an Orlicz-Sobolev Space Setting

In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13].

Multiple brake orbits of even Hamiltonian systems on torus

In this paper,we establish a relationship between the Morse index at rest points in the saddle point reduction and the brake-orbit-type Maslov index at corresponding brake orbits.As an application,we give a criterion to find brake orbits which are contractible and start at{0}×T^n■T^2n for even Hamiltonian on T^2 n by the methods of the Maslov-index theory and a critical point theorem formulated by Bartsch and Wang(1997).Explicitly,if all trivial solutions of a Hamiltonian are nondegenerate in the brake orbit boundary case,there are at least max{iL0(z0)}pairs of nontrivial 1-periodic brake orbits if iL0(z0)>0 or at least max{-iL0(z0)-n}pairs of nontrivial 1-periodic brake orbits if iL0(z0)<-n.In the end,we give an example to find brake orbits for certain Hamiltonian via this criterion.

EXISTENCE OF INFINITE PERIODIC SOLUTIONS TO A KIND OF p-LAPLACIAN DIFFERENTIAL EQUATION WITH DEVIATING ARGUMENTS

In this paper, we study a kind of p-Laplacian differential equation and obtain some new results on the existence of infinite periodic solutions.

EXISTENCE OF THREE SOLUTIONS TO A CLASS OF QUASILINEAR ELLIPTIC SYSTEMS INVOLVING THE(p_1(x), · · ·, p_n(x))-LAPLACIAN

In this paper, we investigate a class of Dirichlet quasilinear elliptic systems involving the(p1(x), ···, pn(x))-Laplacian. Based on the general three critical points theorem of B. Ricceri, we prove the existence of at least three weak solutions to the system.