Existence of Solutions for Discontinuous Functional Equations and Elliptic Boundary-Value Problems
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We prove existence results for discontinuous functional equations in general Lp -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.
CitationCarl, S., & Heikkila, S. (2002). Existence of solutions for discontinuous functional equations and elliptic boundary-value problems. Electronic Journal of Differential Equations, 2002(61), pp. 1-10.
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