Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 08, pp. 1-10.

Title: Solution to a semilinear problem on type II regions
       determined by the Fucik spectrum

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

Abstract: 
 We prove the existence of solutions to the semi-linear problem
 $$\displaylines{
 u''(x)+\alpha u^+(x)+\beta u^-(x)=f(x)\,,\quad x\in (0,\pi)\,,\cr
 u(0)=u(\pi)=0 }
 $$
 where the point $(\alpha,\beta)$ falls in regions of type (II)
 between curves of the Fucik spectrum.
 We use a variational method based on the generalization of the Saddle Point
 Theorem.
 
Submitted October 7, 2002. Published January 28, 2003.
Math Subject Classifications: 35J70, 58E05, 49B27.
Key Words: Resonance; eigenvalue; jumping nonlinearities; Fucik spectrum.