Journal of Inequalities and Applications
Volume 6 (2000), Issue 3, Pages 305-323

Existence theorems for nonlinear elliptic problems

Nikolaos Halidias

National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, Greece

Received 12 September 1999; Revised 9 November 1999

Copyright © 2000 Nikolaos Halidias. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we prove two theorems for noncoercive elliptic boundary value problems using the critical point theory of Chang and the subdifferentiable of Clarke. The first result is for a Dirichlet noncoercive problem and the second one is for Neumann elliptic problem with nonlinear multivalued boundary conditions. We use the mountain-pass and the saddle-point theorems to obtain nontrivial solutions for these problems.