Electron. J. Diff. Eqns., Vol. 2005(2005), No. 29, pp. 1-7.

An Orlicz-Sobolev space setting for quasilinear elliptic problems

Nikolaos Halidias

In this paper we give two existence theorems for a class of elliptic problems in an Orlicz-Sobolev space setting concerning both the sublinear and the superlinear case with Neumann boundary conditions. We use the classical critical point theory with the Cerami (PS)-condition.

Submitted October 14, 2004. Published March 8, 2005.
Math Subject Classifications: 32J15, 34J89, 35J60.
Key Words: Landesman-Laser conditions; critical point theory; nontrivial solution; Cerami (PS) condition; Mountain-Pass Theorem; interpolation inequality.

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Nikolaos Halidias
University of the Aegean
Department of Statistics and Actuarial Science
Karlovassi, 83200, Samos, Greece
email: nick@aegean.gr

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