Existence of multiple positive solutions for Brezis-Nirenberg-type problems involving singular nonlinearities
type: Item
instance of: scholarly article
title: Existence of multiple positive solutions for Brezis-Nirenberg-type problems involving singular nonlinearities
zbMATH Open document ID: 1477.35085
DOI: 10.1155/2021/4709839
author: Mohammed El Mokhtar Ould El Mokhtar
author: Atika Matallah
published in: Journal of Mathematics
publication date: 2021-11-24T00:00:00Z
review text: Summary: This article is devoted to the existence and multiplicity to the following Brezis-Nirenberg-type problems involving singular nonlinearities: \[ \begin{cases} -\Delta u = |u|^{p - 1}u + \lambda(|u|^{-1-\beta}/|x|^\alpha)u & \text{in } \Omega, \\ u = 0 & \text{on } \partial\Omega, \end{cases} \] where \(\Omega\) is a smooth bounded domain in \(\mathbb{R}^N\) (\(N \geq 3\)), \(0\in\Omega\), \(\lambda>0\), \(p= 2^\ast-1\) with \(2^\ast:=2N/(N - 2)\) is the critical Sobolev exponent, \(0\leq\alpha<N(p + \beta)/(p + 1)\), and \(0<\beta<1\). By using the Nehari manifold and maximum principle theorem, the existence of at least two distinct positive solutions is obtained.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 7433068
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/4709839
OpenAlex ID: W3210047863
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description: scientific article; zbMATH DE number 7433068