Electron. J. Diff. Eqns., Vol. 2002(2002), No. 61, pp. 1-10.

Existence of solutions for discontinuous functional equations and elliptic boundary-value problems

Siegfried Carl & Seppo Heikkila

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.

Submitted January 15, 2002. Published June 25, 2002.
Math Subject Classifications: 35J65, 35R05, 35R10.
Key Words: functional equations, elliptic boundary-value problems, discontinuous nonlinearities.

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Siegfried Carl
Current address:
Florida Institute of Technology, Department of Mathematical Sciences,
150 West University Boulevard, Melbourne, FL 32901, USA,
e-mail: scarl@fit.edu
permanent address:
Martin-Luther-Universitat Halle-Wittenberg,
Fachbereich Mathematik und Informatik,
Institut fur Analysis, 06099 Halle, Germany
email: carl@mathematik.uni-halle.de

Seppo Heikkila
Department of Mathematical Sciences, University of Oulu,
Box 3000, FIN-90014, University of Oulu, Finland
Fax: 358 8 5531730. e-mail: sheikki@cc.oulu.fi

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