Abstract
In this work, we study the oscillation of second-order delay differential equations, by employing a refinement of the generalized Riccati substitution. We establish a new oscillation criterion. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. We illustrate the results with some examples.
Highlights
This paper is concerned with oscillation of a second-order differential equation
The oscillations of second order differential equations have been studied by authors and several techniques have been proposed for obtaining oscillation for these equations
0 a (z) w0 (z) + q (z) w (τ (z)) = 0, that was compared with the oscillation of certain first order differential equation and under the condition z0 dz = ∞
Summary
This paper is concerned with oscillation of a second-order differential equation The function f is nondecreasing and satisfies the following conditions f ∈ C (R, R) , w f (w) > 0, f (w) /w ≥ k > 0, for w 6= 0, and lim w→∞ By a solution of Equation (1) we mean a function w ∈ C ([z0 ‚ ∞), R) , zw ≥ z0 , which has the property a (z) [w0 (z)] ∈ C1 ([z0 ‚ ∞), R) , and satisfies Equation (1) on [zw ‚ ∞).
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