On the positive solutions of a higher order functional differential equation with a discontinuity

John R. Graef, Paul W. Spikes and Myron K. Grammatikopoulos

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-11

Abstract:

The n -th order nonlinear functional differential equation [ r ( t ) x ( n − υ ) ( t ) ] ( υ ) = f ( t , x ( g ( t ) ) ) is considered; necessary and sufficient conditions are given for this equation to have: (i) a positive bounded solution x ( t ) → B > 0 as t → ∞ ; and (ii) all positive bounded solutions converging to 0 as t → ∞ . Other results on the asymptotic behavior of solutions are also given. The conditions imposed are such that the equation with a discontinuity [ r ( t ) x ( n − υ ) ( t ) ] ( υ ) = q ( t ) x − λ ,       λ > 0 is included as a special case.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:769678

DOI: 10.1155/S0161171282000234

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