Existence of solutions for discontinuous functional equations and elliptic boundary-value problems - Siegfried Carl (Electronic Journal of Differential Equations, 2002)
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.