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POSITIVE INCREASING SOLUTIONS ON THE HALF-LINE TO SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Published online by Cambridge University Press:  09 August 2007

CH. G. PHILOS
CH. G. PHILOS*
Affiliation:
Department of Mathematics, University of Ioannina, P. O. Box 1186, 451 10 Ioannina, Greece e-mail: cphilos@cc.uoi.gr
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Abstract

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Second order nonlinear delay differential equations with positive delays are considered, and sufficient conditions are given that guarantee the existence of positive increasing solutions on the half-line with first order derivatives tending to zero at infinity. The approach is elementary and is essentially based on an old idea which appeared in the author's paper Arch. Math. (Basel)36 (1981), 168–178. The application of the result obtained to second order Emden-Fowler type differential equations with constant delays and, especially, to second order linear differential equations with constant delays, is also presented. Moreover, some (general or specific) examples demonstrating the applicability of the main result are given.

Keywords

34K1034B1834B40
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 2 , May 2007 , pp. 197 - 211
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

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