On the solvability of some multi-point boundary value problems
type: Item
instance of: scholarly article
title: On the solvability of some multi-point boundary value problems
zbMATH Open document ID: 0858.34013
author: Chaitan P. Gupta
author: Sotiris K. Ntouyas
author: Panagiotis Ch. Tsamatos
published in: Applications of Mathematics
publication date: 1997-03-31T00:00:00Z
full work available at URL: https://eudml.org/doc/32934
review text: The paper deals with the problem of solvability of the multi-point boundary value problem (E), (BC) or (E), (BC)\('\), where \[ x''(t)= f(t,x(t),x'(t))+e(t),\quad t\in (0,1),\tag{E} \] \[ x(0)=\sum^{m-2}_{i=1} c_ix'(\xi_i),\quad x(1)=\sum^{n-2}_{j=1} a_jx(\tau_j),\tag{BC} \] \[ x(0)=\sum^{m-2}_{i=1} c_ix'(\xi_i),\quad x'(1)=\sum^{n-2}_{j=1} a_jx'(\tau_j),\leqno(\text{BC})' \] and the \(c_i\) (resp. \(a_j\)) have the same sign. Using the Leray-Schauder continuation theorem, the authors give conditions on the function \(f\) under which there exists a solution of (E), (BC) or (E), (BC)\('\).
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 894255
zbMATH Keywords: multipoint boundary value problem
zbMATH Keywords: Leray-Schauder continuation theorem
reviewed by: Carmen Simerská
MaRDI profile type: Publication
cites work: Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation
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description: scientific article; zbMATH DE number 894255