Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 113, pp. 1-15.
Title: Oscillation and asymptotic behaviour of a higher order
neutral differential equation with positive and
negative coefficients
Authors: Basak Karpuz (Afyon Kocatepe Univ., Turkey)
Laxmi Narayan Padhy (K.I.S.T., Bhubaneswar, India)
Radhanath Rath (Khallikote Autonomous College, India)
Abstract:
In this paper, we obtain necessary and sufficient conditions so
that every solution of
$$
\big(y(t)- p(t) y(r(t))\big)^{(n)}+
q(t)G( y(g(t)))-u(t)H(y(h(t))) = f(t)
$$
oscillates or tends to zero as $t \to \infty$, where $n$ is
an integer $n \geq 2$, $q>0$, $u\geq 0$.
Both bounded and unbounded solutions are considered in this paper.
The results hold also when $u\equiv 0$, $f(t)\equiv 0$, and
$G(u)\equiv u$.
This paper extends and generalizes some recent results.
Submitted April 4, 2008. Published August 20, 2008.
Math Subject Classifications: 34C10, 34C15, 34K40.
Key Words: Oscillatory solution; neutral differential equation;
asymptotic behaviour.