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elliptic differential inclusions

Proceedings of the Edinburgh Mathematical Society (1)

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Elliptic problems in ℝN with discontinuous nonlinearities
Gabriele Bonanno, Salvatore A. Marano
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 43 / Issue 3 / October 2000

Published online by Cambridge University Press:

20 January 2009, pp. 545-558
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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.