# OSCILLATION AND NONOSCILLATION THEOREMS FOR NONLINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER

• Kim, Rak-Joong ;
• Kim, Dong-Il
• Published : 2007.11.30
• 52 4

#### Abstract

By means of a Riccati transform some oscillation or nonoscillation criteria are established for nonlinear differential equations of second order $$(E_1)\;[p(t)|x#(t)|^{\alpha}sgn\;x#(t)]#+q(t)|x(\tau(t)|^{\alpha}sgn\;x(\tau(t))=0$$. $$(E_2),\;(E_3)\;and\;(E_4)\;where\;0<{\alpha}$$ and $${\tau}(t){\leq}t,\;{\tau}#(t)>0,\;{\tau}(t){\rightarrow}{\infty}\;as\;t{\rightarrow}{\infty}$$. In this paper we improve some previous results.

#### Keywords

Riccati Transform;oscillatory or nonoscillatory property;delay differential equation

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