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Oscillation of third order nonlinear delay dynamic equations on time scales

✍ Scribed by Taher S. Hassan

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
833 KB
Volume
49
Category
Article
ISSN
0895-7177

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✦ Synopsis

It is the purpose of this paper to give oscillation criteria for the third order nonlinear delay dynamic equation

on a time scale T, where Ξ³ β‰₯ 1 is the quotient of odd positive integers, a and r are positive rd-continuous functions on T, and the so-called delay function Ο„ : T β†’ T satisfies Ο„ (t) ≀ t for t ∈ T and lim tβ†’βˆž Ο„ (t) = ∞ and f ∈ C (T Γ— R, R). Our results are new for third order delay dynamic equations and extend many known results for oscillation of third order dynamic equation. These results in the special cases when T = R and T = N involve and improve some oscillation results for third order delay differential and difference equations; when T = hN, T = q N 0 and T = N 2 our oscillation results are essentially new. Some examples are given to illustrate the main results.

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