Existence of positive entire solutions for higher order quasilinear elliptic equations
type: Item
instance of: scholarly article
title: Existence of positive entire solutions for higher order quasilinear elliptic equations
zbMATH Open document ID: 0820.35051
author: Yasuhiro Furusho
author: Takaši Kusano
published in: Journal of the Mathematical Society of Japan
publication date: 1995-09-21T00:00:00Z
review text: The purpose of this paper is to establish the existence of positive non- radial entire solutions for a class of nonlinear elliptic equations of the form \[ (- \Delta)^ Mu = f \bigl( x,u, - \Delta u, \dots, (- \Delta)^{M-1}u \bigr), \quad x \in \mathbb{R}^ N, \tag \(*\) \] where \(M \geq 2\), \(N \geq 2\), \(\Delta\) is the \(N\)-dimensional Laplace operator and \(f\) is a locally Hölder continuous function on \(\mathbb{R}^ N \times \mathbb{R}^ M\), with the aid of the higher order super-subsolution method recently discovered by one of the authors [see \textit{Y. Furusho}, Proc. R. Soc. Edinb., Sect. A 120, No. 1/2, 79-91 (1992; Zbl 0769.35019)]. A crucial step in the development of the paper is the construction of super- and subsolutions of \((*)\) as radial entire solutions of suitable chosen majorants and minorants with radial symmetry of \((*)\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J30
zbMATH DE Number: 757987
zbMATH Keywords: supersolution-subsolution
zbMATH Keywords: positive non-radial entire solutions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04630449
OpenAlex ID: W2012404602
DOI: 10.2969/JMSJ/04630449
description: scientific article; zbMATH DE number 757987