| Autor: |
Pimenta, Marcos T. O., dos Santos, Gelson Conceição G., Santos Júnior, João R. |
| Předmět: |
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| Zdroj: |
Proceedings of the Royal Society of Edinburgh: Section A: Mathematics; Feb2024, Vol. 154 Issue 1, p33-59, 27p |
| Abstrakt: |
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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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