Sufficient conditions for oscillatory behaviour of a first order neutral difference equation with oscillating coefficients.

Rath, R.N.; Misra, N.; Rath, S.K.

Displaying similar documents to “Sufficient conditions for oscillatory behaviour of a first order neutral difference equation with oscillating coefficients.”

On oscillation criteria for third order nonlinear delay differential equations

Ravi P. Agarwal, Mustafa F. Aktas, Aydın Tiryaki (2009)

Archivum Mathematicum

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In this paper we are concerned with the oscillation of third order nonlinear delay differential equations of the form ${(r_{2} (t) {(r_{1} (t) x^{'})}^{'})}^{'} + p (t) x^{'} + q (t) f (x (g (t))) = 0 .$ We establish some new sufficient conditions which insure that every solution of this equation either oscillates or converges to zero.

On the oscillation of third-order quasi-linear neutral functional differential equations

Ethiraju Thandapani, Tongxing Li (2011)

Archivum Mathematicum

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The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation ${[a (t) {({[x (t) + p (t) x (δ (t))]}^{''})}^{α}]}^{'} + q (t) x^{α} (τ (t)) = 0, E$ where $α > 0$ , $0 \leq p (t) \leq p_{0} < \infty$ and $δ (t) \leq t$ . By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results.