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DCDS

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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