Electron. J. Diff. Eqns., Vol. 2001(2001), No. 04, pp. 1-11.

A generalization of the Landesman-Lazer condition

Petr Tomiczek

In this paper we prove the existence of solutions to the semi-linear problem
$$ \displaylines{
 u''(x)+m^2 u(x)+g(x,u(x))=f(x)\cr
 u(0)=u(\pi)=0 }$$
at resonance. We assume a Landesman-Lazer type condition and use a variational method based on the Saddle Point Theorem.

Submitted September 8, 2000. Published January 3, 2001.
Math Subject Classifications: 35J70, 35P30, 47H15.
Key Words: resonance, eigenvalue, Landesman-Lazer condition.

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Petr Tomiczek
Department of Mathematics
University of West Bohemia
Univerzitni 22, 306 14 Plzen, Czech Republic
e-mail: tomiczek@kma.zcu.cz

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