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.