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.

Keywords

• functional equations
• elliptic boundary-value problems
• discontinuous nonlinearities.