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Elliptic problems in ℝN with discontinuous nonlinearities

Published online by Cambridge University Press:  20 January 2009

Gabriele Bonanno  and
Salvatore A. Marano
Gabriele Bonanno
Affiliation:
Dipartimento di Informatica, Matematica, Elettronica e Trasporti, Università di Reggio Calabria, Feo di Vito, 89100 Reggio Calabria, Italy ([email protected])
Salvatore A. Marano
Affiliation:
Dipartimento di Patrimonio Architettonico e Urbanistico, Università di Reggio Calabria, Salita Melissari—Feo di Vito, 89100 Reggio Calabria, Italy ([email protected])
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Abstract

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For a class of elliptic equations in the entire space and with nonlinear terms having a possibly uncountable (but of Lebesgue measure zero) set of discontinuities, the existence of strong solutions is established. Two simple applications are then developed. The approach taken is strictly based on set-valued analysis and fixed-points arguments.

Keywords

elliptic equations in the whole spacediscontinuous nonlinearitieselliptic differential inclusionsimplicit elliptic equationsstrong solutions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 3 , October 2000 , pp. 545 - 558
Copyright
Copyright © Edinburgh Mathematical Society 2000

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