Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

Rok, strany: 2007, 157 - 170

In this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE)

$$ [{r(t)({y(t)-p(t)y({t-τ})})'}]' +q(t) G({y({h(t)})}) = 0 $$

are obtained, where $q, h \in C ([0,∞),\Bbb R)$ such that $q(t) ≥ 0$, $r \in C⁽¹⁾ ([0,∞), (0, ∞))$, $p\in C ([0, ∞),\Bbb R)$, $G \in C (\Bbb R, \Bbb R)$ and $τ \in \Bbb R⁺$. Since the results of this paper hold when $r(t) \equiv 1$ and $G(u) \equiv u$, therefore it extends, generalizes and improves some known results.

ISO 690:

Rath, R., Misra, N., Padhy, L. 2007. Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation. In Mathematica Slovaca, vol. 57, no.2, pp. 157-170. 0139-9918.

APA:

Rath, R., Misra, N., Padhy, L. (2007). Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation. Mathematica Slovaca, 57(2), 157-170. 0139-9918.