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On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
Published online by Cambridge University Press: 28 December 2022
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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 1 , February 2024 , pp. 33 - 59
- Copyright
- Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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