A nonlocal boundary value problem with singularities in phase variables
type: Item
instance of: scholarly article
title: A nonlocal boundary value problem with singularities in phase variables
zbMATH Open document ID: 1068.34019
author: Svatoslav Staněk
published in: Mathematical and Computer Modelling
publication date: 2005-02-22T00:00:00Z
review text: Sufficient conditions for the solvability are obtained for the second-order nonlinear boundary value problem \[ (g(x'(t)))'=f(t,x(t)),\;x'(t)),\quad x(0)=x(T)=-\gamma\min\{x(t): t\in[0,T]\}. \] Here, \(g\) is a continuous increasing odd function. The right-hand side \(f(t,x,x')>0\) may be singular both at \(x=0\) and \(x'=0\). The number \(\gamma\) is positive. The operation of minimum makes the boundary value problem nonlocal. Boundary conditions that fix the minimal and maximal values of a solution to a second-order differential equation were considered by \textit{S. A. Brykalov} [Differ. Equations 29, No.~6, 802--805 (1993; Zbl 0826.34020)].
reviewed by: Sergei A. Brykalov
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2137062
zbMATH Keywords: singular nonlinear second-order differential equation
zbMATH Keywords: nonlocal boundary condition
zbMATH Keywords: solvability
MaRDI profile type: Publication
full work available at URL: j.mcm.2003.11.003
OpenAlex ID: W2108619955
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DOI: 10.1016/J.MCM.2003.11.003
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description: scientific article; zbMATH DE number 2137062