Boundary value problems for a class of quasilinear differential systems with singular nonlinearities
type: Item
instance of: scholarly article
title: Boundary value problems for a class of quasilinear differential systems with singular nonlinearities
zbMATH Open document ID: 0922.34017
author: Zongming Guo
author: Zuodong Yang
published in: Applied Mathematics. Series B (English Edition)
publication date: 1998-11-05T00:00:00Z
review text: Motivated by the study of positive radial solutions to some systems of partial differential equations on annular domains, the authors prove some results on existence and multiplicity of positive solutions to quasilinear differential systems of the form \[ (\varphi_{p}(u'))' + m(t)\varphi_{p}(u') + H_{v}(u,v) - h(t) = 0,\quad(\varphi_{q}(v'))' + n(t)\varphi_{q}(v') + H_{u}(u,v) - k(t) = 0, \] under periodic or Neumann boundary conditions on an interval \((a,b)\). Here, \(\varphi_{\beta}(s) = | s |^{\beta -2}s\), \(p,q > 1\), \(m,n \in L^{\infty}((a,b), \mathbb{R}^{+})\), \(h,k \in L^{1}(a,b)\) and \(H \in C^{1}((0,\infty)\times (0,\infty))\) has a singularity at \(u = 0\) or \(v = 0.\) The main tool used in the proofs is the Leray-Schauder degree theory.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 1193538
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: systems of equations
zbMATH Keywords: radial positive solutions
zbMATH Keywords: existence
zbMATH Keywords: multiplicity
zbMATH Keywords: annular domains
zbMATH Keywords: Leray-Schauder degree
zbMATH Keywords: singular nonlinearities
reviewed by: Antonio Cañada
MaRDI profile type: Publication
full work available at URL: s11766-998-0032-4
OpenAlex ID: W179642938
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DOI: 10.1007/S11766-998-0032-4
description: scientific article; zbMATH DE number 1193538