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April  2000, 6(2): 315-328. doi: 10.3934/dcds.2000.6.315

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

Ana Maria Bertone 1, and  J.V. Goncalves 2,

1. 

Departamento de Matemática, Universidade Federal da Paraiba, 58059-900, João Pessoa(PB), Brazil
2. 

Departamento de Matemática, Universidade de Brasilia, 70910-900, Brasília(DF), Brazil

Received  November 1998 Revised  June 1999 Published  January 2000

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.
Keywords: lower and upper solutions, variational principles., Elliptic problems.
Mathematics Subject Classification: 35B22, 35D05, 35D10, 35J2.
Citation: Ana Maria Bertone, J.V. Goncalves. Discontinuous elliptic problems in $R^N$: Lower and upper solutions and variational principles. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 315-328. doi: 10.3934/dcds.2000.6.315
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