Existence and uniqueness results for an elliptic equation with blowing-up coefficient and lower order term

IF 0.7 Q2 MATHEMATICS Afrika Matematika Pub Date : 2024-07-25 DOI:10.1007/s13370-024-01207-3

Amine Marah

引用次数: 0

Abstract

This paper deals with the existence and uniqueness results for a class of non-coercive Dirichlet elliptic problems whose model example is

$$\begin{aligned} \left\{ \begin{aligned}&-\textrm{div}\Big (\frac{1}{(m-u)^\beta } (1+|u|)^q |\nabla u|^{p-2}\nabla u+c(x)|u|^{p-2}u \sin (u-m)\Big )+g(u)=f\ \ \textrm{in}\ \Omega , \\&u=0\ \ \textrm{on}\ {\partial \Omega },\\ \end{aligned} \right. \end{aligned}$$

where $\Omega $ is a bounded open subset of ${\mathbb {R}}^N (N\ge 2)$, $1< p < N$, $m>0$, $0< \beta <1$, $q>0$, |c| belongs to $L^{\frac{N}{p-1}}(\Omega )$ and g is a continuous function in ${\mathbb {R}}$ which satisfies the sign condition and the data f belongs to $L^1(\Omega )$.

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具有吹胀系数和低阶项的椭圆方程的存在性和唯一性结果

本文讨论了一类非胁迫性 Dirichlet 椭圆问题的存在性和唯一性结果，其模型示例为 $$\begin{aligned} &-\textrm{div}\Big (\frac{1}{(m-u)^\beta })\left\{ \begin{aligned}&-\textrm{div}\Big (\frac{1}{(m-u)^\beta })(1+|u|)^q |\nabla u|^{p-2}\nabla u+c(x)|u|^{p-2}u \sin (u-m)\Big )+g(u)=f\\textrm{in}\\Omega , \&u=0\\textrm{on}\ {\partial \Omega },\\end{aligned}.\（right.\end{aligned}$where $\Omega $ is a bounded open subset of ${\mathbb {R}}^N (N\ge 2)$,$1< p < N$,$m>0$,$0< \beta <1$,$q>；0), |c| belongs to \(L^{frac\{N}{p-1}}(\Omega )$ and g is a continuous function in ${\mathbb {R}}$ which satisfies the sign condition and the data f belongs to $L^1(\Omega )$.

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Afrika Matematika MATHEMATICS-

CiteScore

2.00

自引率

9.10%

发文量