A generalization of the Landesman-Lazer condition

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.

Keywords

• resonance
• eigenvalue
• Landesman-Lazer condition.