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arXiv · 2210.10889

On a quasilinear elliptic problem involving the 1-laplacian operator and a discontinuous nonlinearity

Marcos T. O. Pimenta·Gelson C. G. Santos·João R. Santos Júnior
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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.

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Marcos T. O. Pimenta, Gelson C. G. Santos, João R. Santos Júnior. 2022-10-19. On a quasilinear elliptic problem involving the 1-laplacian operator and a discontinuous nonlinearity. https://arxiv.org/abs/2210.10889

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