Positive solutions for nonlinear singular elliptic equations of \(p\)-Laplacian type with dependence on the gradient
type: Item
instance of: scholarly article
title: Positive solutions for nonlinear singular elliptic equations of \(p\)-Laplacian type with dependence on the gradient
zbMATH Open document ID: 1409.35091
published in: Calculus of Variations and Partial Differential Equations
publication date: 2019-01-10T00:00:00Z
review text: Given a bounded domain \(\Omega\subset \mathbb{R}^N, N \geq 3\), with a \(C^2\)-boundary \(\partial\Omega\), the authors study the following singular elliptic equation with Dirichlet boundary condition \[ \begin{cases} -\Delta_{p} u(x) = f(x,u(x),\nabla u(x))+g(x,u(x)) &\text{in }\Omega,\\ u > 0 &\text{in }\Omega,\\ u=0 &\text{on }\partial \Omega, \end{cases} \] where \(\Delta_p u\) stands for the \(p\)-Laplacian, the convextion term \(f:\Omega\times\mathbb{R}\times \mathbb{R}^N\to\mathbb{R}\) satisfies suitable growth and the semilinear function \(g: \Omega \times (0,\infty)\to\mathbb{R}\) is singular at \(s=0\). Based on the Leray-Schauder alternative principle, the method of sub-supersolution, nonlinear regularity, truncation techniques, and set-valued analysis, the authors prove an existence theorem for positive solutions and show the compactness of the solution set.
reviewed by: Patrick Winkert
Mathematics Subject Classification ID: 35J75
Mathematics Subject Classification ID: 35J91
Mathematics Subject Classification ID: 35J92
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35D35
zbMATH DE Number: 6999929
zbMATH Keywords: singular problems
zbMATH Keywords: convection term
zbMATH Keywords: positive solutions
author: Zhenhai Liu
author: Dumitru Motreanu
author: Sheng-Da Zeng
MaRDI profile type: Publication
full work available at URL: s00526-018-1472-1
OpenAlex ID: W2908499091
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Wikidata QID: Q128651336
DOI: 10.1007/S00526-018-1472-1
description: scientific article; zbMATH DE number 6999929