Electron. J. Diff. Eqns., Vol. 2008(2008), No. 113, pp. 1-15.

Oscillation and asymptotic behaviour of a higher order neutral differential equation with positive and negative coefficients

Basak Karpuz, Laxmi Narayan Padhy, Radhanath Rath

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.

Show me the PDF file (279 KB), TEX file, and other files for this article.

Basak Karpuz
Department of Mathematics, Facaulty of Science and arts,
A.N.S. Campus, Afyon Kocatepe University, 03200 Afyonkarahisar, Turkey
email: bkarpuz@gmail.com
Laxmi Narayan Padhy
Department of Computer Science and Engineering, K.I.S.T,
Bhubaneswar Orissa, India
email: ln_padhy_2006@yahoo.co.in
Radhanath Rath
Department of Mathematics, Khallikote Autonomous College
Berhampur, 760001 Orissa, India
email: radhanathmath@yahoo.co.in

Return to the EJDE web page