A note on quasilinear elliptic eigenvalue problems

Quasilinear Elliptic Systems of Resonant Type and Nonlinear Eigenvalue Problems

Eigenvalue problems for a class of singular quasilinear elliptic equations in weighted spaces

Abstract: In this paper, by using the Galerkin method and the generalized Brouwer’s theorem, some problems of the higher eigenvalues are studied for a class of singular quasiliner elliptic equations in the weighted Sobolev spaces. The existence of weak solutions is obtained for this problem.

ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...

Existence of at least three weak solutions for a quasilinear elliptic system

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

Branches of positive and free boundary solutions for some singular quasilinear elliptic problems

We study the existence and multiplicity of solutions, strictly positive or nonnegative having a free boundary (the boundary of the set where the solution vanishes) of some one-dimensional quasilinear problems of eigenvalue type with possibly singular nonlinear terms. © 2008 Elsevier Inc. All rights reserved.