The generalized logistic equation with indefinite weight driven by the square root of the Laplacian
type: Item
instance of: scholarly article
title: The generalized logistic equation with indefinite weight driven by the square root of the Laplacian
zbMATH Open document ID: 1303.35011
DOI: 10.1088/0951-7715/27/9/2361
author: Alessio Marinelli
author: Dimitri Mugnai
published in: Nonlinearity
publication date: 2014-10-17T00:00:00Z
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 6358224
zbMATH Keywords: indefinite potential
zbMATH Keywords: principal eigenfunction
zbMATH Keywords: nonlinear regularity
zbMATH Keywords: existence and multiplicity theorems
zbMATH Keywords: nonlinear maximum principle
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1088/0951-7715/27/9/2361
OpenAlex ID: W2029623215
review text: The paper deals with the Dirichlet problem NEWLINE\[NEWLINE \begin{cases} \sqrt{-\Delta}u(x)=\lambda \big( \beta(x) u(x)-g(x,u(x)\big) & \mathrm{in}\;\Omega,\\ u(x)=0 & \mathrm{on}\;\partial\Omega \end{cases} NEWLINE\]NEWLINE over a bounded domain \(\Omega\subset \mathbb{R}^N,\) \(N\geq2,\) where \(\beta(x)\) is a sign-changing measurable weight. The authors prove a bifurcation result for the problem considered via regularity estimates when the weight belongs only to certain Lebesgue spaces.
reviewed by: Dian K. Palagachev
description: scientific article; zbMATH DE number 6358224