Sucient conditions in terms of coecient functions have been obtained so that all nonoscillatory solutions along with their first and second derivatives of the third order delay dierential equation y 000 (t) + a(t)y 00 (t) + b(t)y 0 (t) + c(t)y(g(t)) = 0 tend to zero as t ! 1. equations. 1. This paper is concerned with the asymptotic behaviour of nonoscillatory solutions of third order equations of the form y 000 (t) + a(t)y 00 (t) + b(t)y 0 (t) + c(t)y(g(t)) = 0;

background

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Asymptotic behavior of solutions of third order delaydifferential equations

On the asymptotic behaviour of solutions of third order delay differential equations

The objective of this paper is to systematically study oscillation and asymptotic behavior of the third order-nonlinear delay dieren tial equation ( ) (x 00 (t)) 0 + q(t)x ( (t)) = 0; t t0; where q(t) is a positive function, > 0 is a quotient of odd positive integers and the delay function (t) t satises limt!1 (t) = 1. We establish some sucien t 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. AMS (MOS) Subject Classication. 34K11, 34C10.

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Asymptotic behavior of solutions of third order delaydifferential equations

Citations

On the asymptotic behaviour of solutions of third order delay differential equations

Oscillation criteria of hille and nehari types for third-order delay differential equations

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