Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 29, pp. 1-9.
Title: Oscillation of solutions to third-order half-linear neutral
differential equations
Authors: Jozef Dzurina (Technical Univ. of Kosice, Slovakia)
Ethiraju Thandapani (Univ. of Madras, Chennai, India)
Sivaraj Tamilvanan (Univ. of Madras, Chennai, India)
Abstract:
In this article, we study the oscillation of solutions to the
third-order neutral differential equations
$$
\Big(a(t)\big([x(t)\pm p(t)x(\delta(t))]''\big)^\alpha\Big)' +
q(t)x^\alpha(\tau(t)) = 0.
$$
Sufficient conditions are established so that every
solution is either oscillatory or converges to zero.
In particular, we extend the results obtain in [1] for $a(t)$
non-decreasing, to the non-increasing case.
Submitted November 12, 2011. Published February 21, 2012.
Math Subject Classifications: 34K11, 34C10.
Key Words: Third-order neutral differential equation;
Riccati transformation; oscillation of solutions.