Abstract
We investigate oscillatory behavior of solutions to a class of second-order nonlinear neutral delay dynamic equations with nonpositive neutral coefficients. In particular, we study the corresponding noncanonical neutral differential equations. New oscillation criteria are established that complement and improve related contributions to the subject. An example is given to illustrate the main results.
Highlights
1 Introduction Differential, difference equations, and dynamic equations on time scales have an enormous potential for applications in biology, engineering, economics, physics, neural networks, social sciences, etc
Significant attention has been devoted to the oscillation theory of various classes of equations; see, e.g., [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]
We are concerned with the oscillatory behavior of solutions to a second-order neutral dynamic equation r(t) z (t) α + q(t)f x δ(t) = 0, t ∈ [t0, ∞)T, (1.1)
Summary
Differential, difference equations, and dynamic equations on time scales have an enormous potential for applications in biology, engineering, economics, physics, neural networks, social sciences, etc. We are concerned with the oscillatory behavior of solutions to a second-order neutral dynamic equation r(t) z (t) α + q(t)f x δ(t) = 0, t ∈ [t0, ∞)T,. By a solution of (1.1), we mean a function x ∈ Crd[Tx, ∞)T, Tx ∈ [t0, ∞)T, which has the property r(z )α ∈ C1rd[Tx, ∞)T and satisfies (1.1) on [Tx, ∞)T. Many studies have been devoted to the oscillatory behavior of solutions to different classes of equations with nonnegative neutral coefficients; see, e.g., [2, 4, 5, 12, 13, 15, 20] and the references cited therein.
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