Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

HOME ALL ARTICLES View

J. Korean Math. Soc. 2007; 44(6): 1453-1467

Printed November 1, 2007

Copyright © The Korean Mathematical Society.

Oscillation and nonoscillation theorems for nonlinear differential equations of second order

RakJoong Kim and Dong-Il Kim

Hallym University, Hallym University

Abstract

By means of a Riccati transform some oscillation or nonoscillation criteria are established for nonlinear differential equations of second order $$ [p(t)|x'(t)|^{\alpha}\,\text{sgn}\,x'(t)]'+q(t)|x(\tau(t))|^{\alpha} \,\text{sgn}\,x(\tau(t)) =0. \tag{$E_1$} $$ ($E_2$), ($E_3$) and ($E_4$) where $0 < \alpha$ and $$ \tau(t) \le t,\quad \tau'(t)>0,\quad \tau(t)\to\infty~\text{as}~t\to\infty. $$ In this paper we improve some previous results.

Keywords: Riccati transform, oscillatory or nonoscillatory property, delay differential equation

MSC numbers: 34C10, 34C15

Stats or Metrics

Share this article on :

Related articles in JKMS