一类包含1-拉普拉斯算子和不连续非线性的拟线性椭圆问题

IF 0.9 3区数学 Q1 MATHEMATICS

Proceedings of the Royal Society of Edinburgh Section A-Mathematics Pub Date : 2022-10-19 DOI:10.1017/prm.2022.86

M. Pimenta, Gelson C. G. dos Santos, J. R. Santos Júnior

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引用次数: 1

摘要

本文研究了一个包含1-拉普拉斯算子的拟线性椭圆型问题，该问题具有涉及Heaviside函数$H(\cdot - \beta)$的不连续、超线性和亚临界非线性。我们的方法是基于对相关的p-拉普拉斯问题的分析，然后是对p \到1^+$等解的渐近行为的彻底分析。我们还研究了解的渐近性，当$\beta \到0^+$时，我们证明了它收敛于原始问题的解，在非线性中没有不连续。

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

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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来源期刊

Proceedings of the Royal Society of Edinburgh Section A-Mathematics 数学-数学

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations. An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.