Electronic Journal of Differential Equations (Jun 2002)
Existence of solutions for discontinuous functional equations and elliptic boundary-value problems
Abstract
We prove existence results for discontinuous functional equations in general $L^p$-spaces and apply these results to the solvability of implicit and explicit elliptic boundary-value problems involving discontinuous nonlinearities. The main tool in the proof is a fixed point result in lattice-ordered Banach spaces proved by the second author.