A variational characterization of the fucik spectrum and applications

Abstract

We characterize the {\it Fucik spectrum} (see \cite{fucik}) of a class selfadjoint operators. Our characterization relies on Lyapunov-Schmidt reduction arguments. We use this characterization to establish the existence of solutions for a semilinear wave equation. This work has been motivated by the authors' results in \cite{chcastro1} where one dimensional second order ordinary differential equations are studied.