Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 04, pp. 1-11.

Title: A generalization of the  Landesman-Lazer condition

Author: Petr Tomiczek (Univ. of West Bohemia, Plzen, Czech Republic)
          
Abstract: 
 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.