Abstract
Some oscillation criteria are established for the second order nonlinear neutral differential equations of the form ((x(t) + ax(t �1) bx(t + �2)) � ) 00 = q(t)x � (t �1) + p(t)x � (t + �2), and (x(t) ax(t �1) + bx(t + �2) � ) 00 = q(t)x � (t �1) + p(t)x � (t + �2) whereandare the ratios of odd positive integers with � � 1. Examples are provided to illustrate the main results.
Highlights
In this paper we study the oscillatory behavior of all solutions of neutral differential equations of the form
Where t ≥ t0 ≥ 0, a and b are nonnegative constants, τ1, τ2, σ1 and σ2 are positive constants, q(t), p(t) ∈ C ([t0, ∞), [t0, ∞)), α, and β are the ratios of odd positive integers with β ≥ 1
We shall obtain some sufficient conditions for the oscillation of all solutions of the equations (1.1) and (1.2)
Summary
In this paper we study the oscillatory behavior of all solutions of neutral differential equations of the form We shall obtain some sufficient conditions for the oscillation of all solutions of the equations (1.1) and (1.2). Assume that x(t) is a nonoscillatory solution of equation (1.1).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
