Existence of a positive radial solution for semilinear elliptic problem involving variable exponent

IF 1 4区数学 Q1 MATHEMATICS

Electronic Research Archive Pub Date : 2023-01-01 DOI:10.3934/era.2023125

Changmu Chu, Shan Li, H. Suo

引用次数: 0

Abstract

This paper consider that the following semilinear elliptic equation

0.1 \begin{document}$ \begin{equation} \left\{ \begin{array}{ll} -\Delta u = u^{q(x)-1}, &\ \ {\mbox{in}}\ \ B_1,\\ u>0, &\ \ {\mbox{in}}\ \ B_1,\\ u = 0, &\ \ {\mbox{in}}\ \ \partial B_1, \end{array} \right. \end{equation} $\end{document}

where $ B_1 $ is the unit ball in $ \mathbb{R}^N(N\geq 3) $, $ q(x) = q(|x|) $ is a continuous radial function satifying $ 2\leq q(x) < 2^* = \frac{2N}{N-2} $ and $ q(0) > 2 $. Using variational methods and a priori estimate, the existence of a positive radial solution for (0.1) is obtained.

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变指数半线性椭圆型问题径向正解的存在性

This paper consider that the following semilinear elliptic equation 0.1 \begin{document}$ \begin{equation} \left\{ \begin{array}{ll} -\Delta u = u^{q(x)-1}, &\ \ {\mbox{in}}\ \ B_1,\\ u>0, &\ \ {\mbox{in}}\ \ B_1,\\ u = 0, &\ \ {\mbox{in}}\ \ \partial B_1, \end{array} \right. \end{equation} $\end{document} where $ B_1 $ is the unit ball in $ \mathbb{R}^N(N\geq 3) $, $ q(x) = q(|x|) $ is a continuous radial function satifying $ 2\leq q(x) < 2^* = \frac{2N}{N-2} $ and $ q(0) > 2 $. Using variational methods and a priori estimate, the existence of a positive radial solution for (0.1) is obtained.

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

Electronic Research Archive MATHEMATICS-

CiteScore

1.30

自引率

12.50%

发文量

170