OSCILLATION CRITERIA OF HILLE AND NEHARI TYPES FOR THIRD-ORDER DELAY DIFFERENTIAL EQUATIONS

TitleOSCILLATION CRITERIA OF HILLE AND NEHARI TYPES FOR THIRD-ORDER DELAY DIFFERENTIAL EQUATIONS
Publication TypeJournal Article
Year of Publication2007
AuthorsSAKER, SH
Secondary TitleCommunications in Applied Analysis
Volume11
Issue4
Start Page451
Pagination468
Date Published12/2007
Type of Workscientific: mathematics
ISSN1083–2564
AMS34C10., 34K11
Abstract

The objective of this paper is to systematically study oscillation and asymptotic behavior of the third order-nonlinear delay differential equation

where q(t) is a positive function, γ > 0 is a quotient of odd positive integers and the delay function τ (t) ≤ t satisfies limt→∞ τ (t) = ∞. We establish some sufficient conditions of Hille and Nehari types, which ensure that (∗) is oscillatory or the solutions converge to zero. Our results in the nondelay case extend and improve some known results in the literature and in the delay case the results can be applied to new classes of equations which are not covered by the known criteria. Some examples are considered to illustrate the main results.
URLhttp://www.acadsol.eu/en/articles/11/4/3.pdf
Short TitleTHIRD ORDER DIFFERENTIAL EQUATIONS
Refereed DesignationRefereed
Full Text

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