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Bulletin of the London Mathematical Society Advance Access originally published online on August 11, 2009
Bulletin of the London Mathematical Society 2009 41(5):872-884; doi:10.1112/blms/bdp064
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© 2009 London Mathematical Society

Positive solutions to a higher-order nonlinear delay boundary value problem on the half-line

Ch. G. Philos

Department of Mathematics
University of Ioannina
P.O. Box 1186
451 10 Ioannina
Greece

Received 3 November 2008. Revision received 20 May 2009.

The main result of this paper establishes sufficient conditions that guarantee the existence of positive solutions to a boundary value problem on the half-line for nth-order (n > 2) nonlinear differential equations with positive delays. The application of the main result to the particular case of Emden–Fowler-type differential equations with constant delays as well as to the special case of linear differential equations with constant delays, is also presented. Moreover, some (general or specific) examples demonstrating the applicability of our result are included.

2000 Mathematics Subject Classification 34K10, 34B18, 34B40.

Dedicated to Professor Gerry Ladas on the Occasion of His 72th Birthday


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