Positive solutions for a semipositone anisotropic p-Laplacian problem

IF 1.7 4区 数学 Q1 Mathematics
A. Razani, Giovany M. Figueiredo
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引用次数: 0

Abstract

In this paper, a semipositone anisotropic p-Laplacian problem $$ -\Delta _{\overrightarrow{p}}u=\lambda f(u), $$ on a bounded domain with the Dirchlet boundary condition is considered, where $A(u^{q}-1)\leq f(u)\leq B(u^{q}-1)$ for $u>0$ , $f(0)<0$ and $f(u)=0$ for $u\leq -1$ . It is proved that there exists $\lambda ^{*}>0$ such that if $\lambda \in (0,\lambda ^{*})$ , then the problem has a positive weak solution $u_{\lambda}\in L^{\infty}(\overline{\Omega})$ via combining Mountain-Pass arguments, comparison principles, and regularity principles.
半正交各向异性 p-Laplacian 问题的正解
本文考虑了一个半正交各向异性 p-Laplacian 问题 $$ -\Delta _{overrightarrow{p}}u=\lambda f(u), $$ 在具有 Dirchlet 边界条件的有界域上,其中 $A(u^{q}-1)\leq f(u)\leq B(u^{q}-1)$ 对于 $u>0$ 、$f(0)0$ 如果 $\lambda \in (0,\lambda ^{*})$,那么通过结合山-帕斯论证、比较原则和正则性原则,问题在 L^{in\fty}(\overline{Omega})$ 有一个正的弱解 $u_{\lambda}\in。
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
Boundary Value Problems
Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.00
自引率
5.90%
发文量
83
审稿时长
4 months
期刊介绍: The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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