Oscillation theorems for second-order superlinear neutral differential equations

✍ Scribed by Blanka Baculíková, Tongxing Li, Jozef Džurina

• Book ID: 119932469
• Publisher: SP Versita
• Year: 2013
• Tongue: English
• Weight: 202 KB
• Volume: 63
• Category: Article
• ISSN: 0139-9918
• DOI: 10.2478/s12175-012-0087-9

✦ Synopsis

Abstract

The purpose of this paper is to investigate the oscillation of the second-order neutral differential equations of the form (E)$$
(r(t)|z'(t)|^{\alpha - 1} z'(t))' + q(t)|x(\sigma (t))|^{\alpha - 1} x(\sigma (t)) = 0,
$$ where z(t) = x(t) + p(t)x(τ(t)). The obtained comparison principles essentially simplify the examination of the studied equations. Further, our results extend and improve the results in the literature.