Electron. J. Diff. Eqns., Vol. 2003(2003), No. 08, pp. 1-10.

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

Petr Tomiczek

We prove the existence of solutions to the semi-linear problem
 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.

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Petr Tomiczek
Department of Mathematics
University of West Bohemia
Univerzitni 22, 306 14 Plzen, Czech Republic
e-mail: tomiczek@kma.zcu.cz

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