Abstract
The oscillatory behavior of the solutions to a differential equation with several non-monotone arguments and nonnegative coefficients is studied, and some new oscillation criteria are given. More precisely, sufficient conditions in terms of limsup and liminf are established, which essentially improve several known criteria existing in the literature. The results are illustrated by examples numerically solved in MATLAB.
Highlights
Consider the first-order linear differential equation with several variable deviating arguments of either delayed (DDE)m x (t) + pi(t)x τi(t) = 0, t ≥ t0, (E)i=1 or advanced type (ADE)m x (t) – qi(t)x σi(t) = 0, t ≥ t0, (E )i=1 where pi, qi, 1 ≤ i ≤ m, are functions of nonnegative real numbers, and τi, σi, 1 ≤ i ≤ m, are functions of positive real numbers satisfying τi(t) < t, t ≥ t0 and lim t→∞ τi (t) = ∞, 1 ≤ i ≤ m
An equation is oscillatory if all its solutions oscillate
Our results essentially improve several known criteria existing in the literature, which are briefly reviewed below for the reader’s convenience
Summary
An equation is oscillatory if all its solutions oscillate. The problem of establishing sufficient conditions for the oscillation of all solutions of equations (E) or (E ) has been studied extensively. The objective of this paper is to derive new sufficient conditions for all solutions of (E) and (E ) to be oscillatory when the arguments are not necessarily monotone.
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