Existence of solutions for first order ordinary differential equations with nonlinear boundary conditions
type: Item
instance of: scholarly article
title: Existence of solutions for first order ordinary differential equations with nonlinear boundary conditions
zbMATH Open document ID: 1058.34015
DOI: 10.1016/S0096-3003(03)00678-7
author: Donal O'Regan
author: Daniel Franco
author: Juan J. Nieto
published in: Applied Mathematics and Computation
publication date: 2004-08-06T00:00:00Z
review text: The paper deals with solutions of the nonlinear equation \[ u'(t)= F(t,u(t)), \qquad t\in I= [0,T], \quad T> 0, \tag{1} \] where \(F: [0,T]\times \mathbb{R}\to \mathbb{R}\) and \(g: \mathbb{R}^2\to \mathbb{R}\) are continuous functions. The goal of the authors is to present a new existence result for solutions of (1) satisfying \(g(u(0),u(T))= 0\). To this end, they introduce a new concept of coupled lower and upper solutions that allow them to obtain a pair of quasisolutions. Under suitable assumptions on \(F\) and \(g\), the authors show the existence of such solutions.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2082117
zbMATH Keywords: antiperiodic solutions
zbMATH Keywords: nonlinear boundary conditions
zbMATH Keywords: upper and lower solutions
Wikidata QID: Q60199451
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2082117