Nonlinear spectra: The Neumann problem

Abstract

Eigenvalue problems of the form x” = −λf(x⁺ ) + μg(x⁻ ), x‘(a) = 0, x^' (b) = 0 are considered. We are looking for (λ,μ) such that the problem (i), (ii) has a nontrivial solution. This problem generalizes the famous Fučík problem for piece‐wise linear equations. In our considerations functions f and g may be nonlinear. Consequently spectra may differ essentially from those for the Fučík equation.

First published online: 14 Oct 2010