Existence of global solutions to nonlinear mixed-type functional differential equations. (June 2020)

• Record Type: Journal Article
• Authors: Diblík, J.; Vážanová, G.
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: Global solution -- Mixed-type functional differential equation -- Advance-delay functional differential equation -- Schauder–Tychonoff fixed point theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111731
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The paper considers systems of nonlinear mixed-type functional differential equations. It aims to find conditions for the existence of global solutions with graphs staying in a prescribed domain. A relevant result is proved by Schauder–Tychonoff fixed-point technique with illustrative examples shown. A linear variant of the derived result is formulated, comparisons with known results are discussed and some open problems are formulated.