Existence of Solutions for Discontinuous Functional Equations and Elliptic Boundary-Value Problems
Southwest Texas State University, Department of Mathematics
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.
Functional equations, Elliptic boundary-value problems, Discontinuous nonlinearities
Carl, S., & Heikkila, S. (2002). Existence of solutions for discontinuous functional equations and elliptic boundary-value problems. <i>Electronic Journal of Differential Equations, 2002</i>(61), pp. 1-10.