Nonlocal boundary vector value problems for ordinary differential systems of higher order
type: Item
instance of: scholarly article
title: Nonlocal boundary vector value problems for ordinary differential systems of higher order
zbMATH Open document ID: 1019.34009
DOI: 10.1016/S0362-546X(01)00906-3
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-11-28T00:00:00Z
review text: The authors study the existence of solutions to a \(n\)th-order \(m\)-dimensional ordinary differential system of the type \[ x^{(n)}=f(t, x, x', \ldots , x^{(n-1)}),\qquad t\in I, \tag{1} \] where \(I\) stands for the interval \([0, 1]\) and \(f: I\times (\mathbb{R}^{n})^{n} \to \mathbb{R}^{m}\) is a Carathéodory function, satisfying the following nonlocal boundary value conditions \[ x^{(j)} (0) = 0, \qquad j = 0, 1, \ldots , k-1, \tag{2} \] \[ x^{(j)} (1) = \int \limits^{1}_{0} [d G_{n-j}(s)]x^{j}(s), \qquad j = k, k+1, \ldots , n-1, \tag{3} \] for a certain fixed number \(k \in {1, 2, \ldots , n-1}\), where the integral is in the sense of Riemann-Stieltjes. In this article, the authors apply the Leray-Schauder continuation theorem to derive sufficient conditions for the existence of solutions to the boundary value problem (1)--(3).
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 1836654
zbMATH Keywords: higher-order differential equations
zbMATH Keywords: nonlocal boundary value problems
zbMATH Keywords: existence
zbMATH Keywords: nonexestence
author: George Karakostas
author: Panagiotis Ch. Tsamatos
MaRDI profile type: Publication
cites work: Q3712561
cites work: Q5579204
cites work: Q5688223
cites work: Existence results for \(m\)-point boundary value problems
cites work: Q3820938
cites work: Q3049152
cites work: Existence and unicity of solutions of n-point boundary value problems
full work available at URL: s0362-546x(01)00906-3
OpenAlex ID: W2002501631
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description: scientific article; zbMATH DE number 1836654