Positive solutions of singular boundary value problems for nonlinear differential systems
type: Item
instance of: scholarly article
title: Positive solutions of singular boundary value problems for nonlinear differential systems
zbMATH Open document ID: 1127.34011
author: Bingmei Liu
author: Lishan Liu
author: Yonghong Wu
published in: Applied Mathematics and Computation
publication date: 2007-06-06T00:00:00Z
review text: Consider the boundary value problem \[ \begin{gathered} -x''(t)= f(t, y)\quad\text{for }t\in (0,1),\\ -y''(t)= g(t, x)\quad\text{for }t\in (0,1),\\ \alpha_1 x(0)- \beta_1 x'(0)= \gamma_1 x(1)+ \delta_1 x'(1)= 0,\\ \alpha_2 y(0)- \beta_2 y'(0)= \gamma_2 y(1)+\delta_2 y'(1)= 0,\end{gathered}\tag{\(*\)} \] where \(\alpha_i\), \(\beta_i\), \(\gamma_i\), \(\delta_i\) are nonnegative constants and \(\rho_i= \alpha_i\gamma_i+ \alpha_i\delta_i+ \gamma_i\beta_i> 0\) for \(i= 1,2\). The functions \(f\) and \(g\) may be singular at \(t= 0\), \(t= 1\), \(x= 0\), \(y= 0\). The authors construct a special cone and apply fixed point index theory in a cone to establish the existence of at least one positive solution of \((*)\).
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47H11
zbMATH DE Number: 5161971
zbMATH Keywords: differential systems
zbMATH Keywords: positive solutions
zbMATH Keywords: singular
zbMATH Keywords: boundary value problems
MaRDI profile type: Publication
full work available at URL: j.amc.2006.08.060
OpenAlex ID: W2048922683
cites work: A coupled system of boundary value problems
cites work: Twin solutions to singular Dirichlet problems
cites work: Existence of solutions for nonlinear singular boundary value problems
cites work: Multiple positive solutions of some boundary value problems
cites work: Q3994493
cites work: Nonnegative solutions to some singular second-order boundary value problems
cites work: Positive solutions of semilinear differential equations with singularities
cites work: Q3414039
cites work: Multiple positive solutions of nonlinear singular boundary value problem for fourth-order equations.
cites work: Multiple solutions of singular boundary value problems for differential systems
cites work: Positive solutions for singular boundary value problems of a coupled system of differential equations
cites work: Multiple nonnegative solutions of second-order systems of boundary value problems
cites work: Multiplicity of positive radial solutions for an elliptic system on an annulus
cites work: On the number of positive solutions of nonlinear systems.
DOI: 10.1016/J.AMC.2006.08.060
description: scientific article; zbMATH DE number 5161971