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.