Abstract
In this work, we study a quasilinear elliptic problem involving the 1-Laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function
$H(\cdot - \beta )$
. Our approach is based on an analysis of the associated p-Laplacian problem, followed by a thorough analysis of the asymptotic behaviour or such solutions as
$p \to 1^+$
. We study also the asymptotic behaviour of the solutions, as
$\beta \to 0^+$
and we prove that it converges to a solution of the original problem, without the discontinuity in the nonlinearity.
Publisher
Cambridge University Press (CUP)
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Cited by
2 articles.
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