Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 94, pp. 1-12.

Title: Potential Landesman-Lazer type conditions and the
       Fucik spectrum

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

Abstract: 
 We prove the existence of solutions to the nonlinear problem
 $$\displaylines{
 u''(x)+\lambda_+ u^+(x)-\lambda_- u^-(x)+g(x,u(x))=f(x)\,,\quad
 x\in (0,\pi)\,,\cr
 u(0)=u(\pi)=0 }
 $$
 where the point $[\lambda_+,\lambda_-]$ is a point of the Fucik
 spectrum  and the nonlinearity $g(x,u(x))$ satisfies a potential
 Landesman-Lazer type  condition.
 We use a variational method based on the generalization of the
 Saddle Point Theorem.
  
Submitted November 26, 2004. Published August 29, 2005.
Math Subject Classifications: 35J70, 58E05, 49B27.
Key Words: Resonance; eigenvalue; jumping nonlinearities; Fucik spectrum.