On some polyharmonic elliptic equation with discontinuous and increasing nonlinearities
type: Item
instance of: scholarly article
title: On some polyharmonic elliptic equation with discontinuous and increasing nonlinearities
zbMATH Open document ID: 1381.35034
author: Sami Aouaoui
published in: Applied Mathematics Letters
publication date: 2017-11-16T00:00:00Z
review text: The paper studies the problem \((-\Delta )^m u=f(x,u)+\lambda h(x)\) in \(\mathbb R^N\), where \(N\geq 5\). Here \(m\in N\), \(2\leq m<N/2\), \(\lambda >0\), \(h\in L^{2N/(N+2m)}(\mathbb R^N)\), \(h\neq 0\). Under some assumption on \(f\) it is shown that there exists \(\lambda_* >0\) such that for \(0<\lambda <\lambda_*\) the problem admits at least one nontrivial solution.
reviewed by: Dagmar Medková
Mathematics Subject Classification ID: 35J30
Mathematics Subject Classification ID: 31B30
zbMATH DE Number: 6807758
zbMATH Keywords: polyharmonic equation
zbMATH Keywords: existence of solutions
MaRDI profile type: Publication
full work available at URL: j.aml.2017.06.011
OpenAlex ID: W2733964984
cites work: A method to solve discontinuous boundary value problems.
cites work: Elliptic problems with lack of compactness via a new fixed point theorem
cites work: On a nonlocal elliptic problem involving critical growth
cites work: Quasilinear elliptic problems with critical exponents and discontinuous nonlinearities
cites work: Existence of solutions to equations ofN-Laplacian type with Trudinger–Moser nonlinearities
cites work: On a class of quasilinear elliptic problems involving Trudinger-Moser nonlinearities
cites work: On a class of nonhomogeneous fractional quasilinear equations in \(\mathbb R^n\) with exponential growth
cites work: Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
cites work: Q3845569
DOI: 10.1016/J.AML.2017.06.011
description: scientific article; zbMATH DE number 6807758