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Global solutions of a singular initial value problem to second order nonlinear delay differential equations

Authors
Journal
Mathematical and Computer Modelling
0895-7177
Publisher
Elsevier
Publication Date
Volume
43
Identifiers
DOI: 10.1016/j.mcm.2005.12.005
Keywords
  • Delay Differential Equation
  • Initial Value Problem
  • Global Solution
  • Schauder’S Fixed Point Theorem
  • Banach’S Contraction Principle
Disciplines
  • Mathematics

Abstract

Abstract The paper is concerned with an initial value problem to second order nonlinear singular delay differential equations. By the use of the Schauder fixed point theorem, a result for the existence of global solutions is derived. Also, via the Banach contraction principle, another result concerning the existence and uniqueness of global solutions is established. Moreover, applications of these results to a particular case of second order nonlinear singular delay differential equations as well as to the special case of second order nonlinear singular ordinary differential equations are presented. Finally, some specific applications to certain equations and two examples are given to demonstrate the applicability of the results of the paper.

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