Positive solutions for a second-order nonlinear coupled system with derivative dependence subject to coupled Stieltjes integral boundary conditions
type: Item
instance of: scholarly article
title: Positive solutions for a second-order nonlinear coupled system with derivative dependence subject to coupled Stieltjes integral boundary conditions
zbMATH Open document ID: 1494.34105
author: Yanyan Li
published in: Mediterranean Journal of Mathematics
publication date: 2022-03-14T00:00:00Z
review text: The paper is concerned with the second-order differential system with nonlinearities depending on the first derivatives, subject to coupled Riemann-Stieltjes integral boundary conditions \[\left\{\begin{array}{l} -u''(t)=f_1(t,u(t),v(t),u'(t),v'(t)),\,\,\,t\in [0,1],\\ -v''(t)=f_2(t,u(t),v(t),u'(t),v'(t)),\,\,\,t\in [0,1],\\ u(0)=\alpha[v],\,\,\,u'(1)=\beta[u],\\ v(0)=\beta[u],\,\,\,v'(1)=\alpha[v], \end{array}\right.\leqno(1)\] where \(\alpha\) and \(\beta\) are linear functionals given by \(\alpha[u]=\int_0^1u(t)dA(t)\), \(\beta[u]=\int_0^1u(t)dB(t)\), and \(A,\,B\) are bounded variation functions. Under some assumptions on the functions \(f_1\) and \(f_2\), and on the spectral radius of an associated linear operator, the authors prove the existence of positive solutions for problem \((1)\), by using the fixed point index theory.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7488606
zbMATH Keywords: positive solution
zbMATH Keywords: fixed point index
zbMATH Keywords: cone
zbMATH Keywords: spectral radius
reviewed by: Rodica Luca
MaRDI profile type: Publication
full work available at URL: s00009-022-01977-9
OpenAlex ID: W4211080300
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DOI: 10.1007/S00009-022-01977-9
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description: scientific article; zbMATH DE number 7488606