Boundary and periodic value problems for systems of differential equations under Bernstein-Nagumo growth condition
type: Item
instance of: scholarly article
title: Boundary and periodic value problems for systems of differential equations under Bernstein-Nagumo growth condition
zbMATH Open document ID: 0831.34021
published in: Differential and Integral Equations
publication date: 1996-02-12T00:00:00Z
review text: The author establishes several existence results for systems of second- order differential equations (1) \(x'' = f(t,x,x')\) subjected on the interval \(0,1\) to various boundary conditions (e.g. nonhomogeneous Dirichlet, Neumann, Sturm-Liouville conditions, periodic conditions). It is assumed that \(f : 0,1 \times \mathbb{R} 2n \to \mathbb{R} n\) fulfils the Carathéodory conditions and some (Bernstein-type or Nagumo-type) growth conditions. Proofs are obtained via the theory of topological transversality for continuous compact operators in the case of the Bernstein-type conditions and for upper semi-continuous, compact, multivalued operators in the case of the Nagumo-type conditions. On the contrary to the previously published results concerning the subject, Hartman's condition is replaced by another condition which is automatically satisfied in the scalar case.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 775647
zbMATH Keywords: boundary value problem
zbMATH Keywords: periodic solution
zbMATH Keywords: Bernstein-type growth conditions
zbMATH Keywords: Nagumo-type growth conditions
zbMATH Keywords: second-order differential equations
zbMATH Keywords: topological transversality
author: Marlène Frigon
reviewed by: Milan Tvrdý
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 775647