DCDS
Discontinuous elliptic problems in $R^N$: Lower and upper solutions and variational principles
Ana Maria Bertone J.V. Goncalves
Discrete & Continuous Dynamical Systems - A 2000, 6(2): 315-328 doi: 10.3934/dcds.2000.6.315
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

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