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On the existence of positive solutions on the half-line to nonlinear two-dimensional delay differential systems

Published online by Cambridge University Press:  23 September 2009

Ch. G. Philos
Affiliation:
Department of Mathematics, University of Ioannina, PO Box 1186, 45110 Ioannina, Greece; Email: ([email protected])
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Abstract

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This paper is concerned with a boundary-value problem on the half-line for nonlinear two-dimensional delay differential systems with positive delays. A theorem is established, which provides sufficient conditions for the existence of positive solutions. The application of this theorem to the special case of second-order nonlinear delay differential equations is given. Also, the application of the theorem to two-dimensional Emden–Fowler-type delay differential systems with constant delays is presented. Moreover, some general examples demonstrating the applicability of the theorem are included.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2009