Fourth-order \(p\)-Laplacian nonlinear systems via the vector version of Krasnosel'skiĭ's fixed point theorem
type: Item
instance of: scholarly article
title: Fourth-order \(p\)-Laplacian nonlinear systems via the vector version of Krasnosel'skiĭ's fixed point theorem
zbMATH Open document ID: 1193.47057
author: T. Moussaoui
author: Smail Djebali
author: Radu Precup
published in: Mediterranean Journal of Mathematics
publication date: 2010-01-18T00:00:00Z
review text: The paper deals with the fourth-order nonlinear differential system with \(p\)-Laplacian \[ \begin{cases}(\varphi_p(u_1''))''=\lambda_1a_1(t)f_1(u_1,u_2),\;t\in (0,1),\\ (\varphi_p(u_2''))''=\lambda_2a_2(t)f_2(u_1,u_2),\;t\in (0,1),\\ u_1(0)=u_1(1)=u_1''(0)=u_1''(1)=0,\\ u_2(0)=u_2(1)=u_2''(0)=u_2''(1)=0,\end{cases}\tag{1} \] where \(f_i\in C([0,+\infty)^2,[0,+\infty))\), \(a_i\in C([0,1],[0,+\infty))\), \(\lambda_i\) are positive parameters for \(i=1,2\) and \(\varphi_p(s)=s|s|^{p-2}\), \(p>1\). By using Krasnoselskii's fixed point theorem and a vector version of it, the authors present sufficient conditions for the existence of positive solutions of \((1)\).
reviewed by: Rodica Luca
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 5659719
zbMATH Keywords: fourth-order equation
zbMATH Keywords: Krasnosel'skij's cone fixed point theorem
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: positive solution
zbMATH Keywords: compression and expansion
MaRDI profile type: Publication
full work available at URL: s00009-009-0017-4
OpenAlex ID: W2036061334
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DOI: 10.1007/S00009-009-0017-4
description: scientific article; zbMATH DE number 5659719