Discontinuous elliptic problems in $R^N$: Lower and upper solutions and variational principles

Ana Maria Bertone; J.V. Goncalves

doi:10.3934/dcds.2000.6.315

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2000, Volume 6, Issue 2: 315-328. Doi: 10.3934/dcds.2000.6.315

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Discontinuous elliptic problems in $R^N$: Lower and upper solutions and variational principles

Ana Maria Bertone¹ and
J.V. Goncalves^2,

1.
Departamento de Matemática, Universidade Federal da Paraiba, 58059-900, João Pessoa(PB)
2.
Departamento de Matemática, Universidade de Brasilia, 70910-900, Brasília(DF)

Received: November 1998

Revised: June 1999

Published: April 2000

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Abstract

This paper deals with existence and regularity of positive solutions of sublinear equations of the form $-\Delta u + b(x)u =\lambda f(u)$ in $\Omega$ where either $\Omega\in R^N$ is a bounded smooth domain in which case we consider the Dirichlet problem or $\Omega =R^N$, where we look for positive solutions, $b$ is not necessarily coercive or continuous and $f$ is a real function with sublinear growth which may have certain discontinuities. We explore the method of lower and upper solutions associated with some subdifferential calculus.

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Mathematics Subject Classification: 35B22, 35D05, 35D10, 35J20.

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