Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840592 | Nonlinear Analysis: Theory, Methods & Applications | 2012 | 17 Pages |
Abstract
In this paper we establish the existence of two nontrivial weak solutions of some eigenvalue problems, involving a general elliptic operator in divergence form. First we study a one parameter problem under homogeneous Dirichlet boundary conditions in bounded domains, and then a two parameters problem under inhomogeneous nonlinear Robin boundary conditions in regular bounded domains. These results complete in several directions some recent papers, where a Ricceri type critical point theorem was used. The main argument of this paper is based on two recent theorems due to Arcoya and Carmona (2007) in [2] which we use in a slightly modified version, see Section 2.
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Authors
Francesca Colasuonno, Patrizia Pucci, Csaba Varga,