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

Authors:
R. P. Agarwal;Ch. G. Philos;P. Ch. Tsamatos
Affiliations:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA;Department of Mathematics, University of Ioannina, P.O. Box 1186, 451 10 Ioannina, Greece;Department of Mathematics, University of Ioannina, P.O. Box 1186, 451 10 Ioannina, Greece
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2006

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The existence of multiple positive solutions to boundary value problems of nonlinear delay differential equations with countably many singularities on infinite interval

Journal of Computational and Applied Mathematics

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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.