Existence of positive solution for elliptic equations with singular terms and combined nonlinearities
type: Item
instance of: scholarly article
title: Existence of positive solution for elliptic equations with singular terms and combined nonlinearities
zbMATH Open document ID: 1479.35454
author: Marcelo Montenegro
author: Jesus Alberto Leon Tordecilla
published in: Journal of Mathematical Analysis and Applications
publication date: 2021-07-23T00:00:00Z
review text: This paper studies the following boundary value problem \[ \begin{cases} -\Delta u+u^\gamma=\lambda u^{-q_1}+u^{p_1}\text{ in }\Omega,\\ u>0\text{ in }\Omega,\\ \frac{\partial u}{\partial \nu}=\mu u^{-q_2}+u^{p_2}\text{ on }\partial\Omega. \end{cases} \] Here \(0<q_i<1\), \(i=1,2\), \(\lambda\) and \(\mu\) are positive parameters, \(\Omega\) is a smooth bounded domain in \(\mathbb{R}^N\), \(N\ge 2\), and if \(N\ge 3\), then \(1\leq\gamma<\frac{N+2}{N-2}\), \(1<p_1<\frac{N+2}{N-2}\), \(1<p_2<\frac{N}{N-2}\), and if \(N=2\), then \(1\,\gamma<\infty\), \(1<p_1<\infty\), \(1<p_2<\infty\). The existence and nonexistence of positive solutions for this problem are proved using an approximation scheme, sub-super solution and Perron's method. The asymptotic behavior of the solutions with respect to the parameters is also investigated.
reviewed by: Shuangjie Peng
Mathematics Subject Classification ID: 35J75
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 7374569
zbMATH Keywords: singular elliptic equations
zbMATH Keywords: existence of positive solutions
zbMATH Keywords: asymptotic behavior
MaRDI profile type: Publication
full work available at URL: j.jmaa.2021.125316
OpenAlex ID: W3162877550
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DOI: 10.1016/J.JMAA.2021.125316
description: scientific article; zbMATH DE number 7374569