New oscillation tests and some refinements for first-order delay dynamic equations

Abstract

Abstract:In this paper, we present new sufficient conditions for the oscillation of first-order delay dynamic equations on time scales. We also present some examples to which none of the previous results in the literature can apply.

Oscillatory behaviour of higher-order nonlinear neutral delay dynamic equations on time scales

“…In view of Theorem 1 and Theorem 2 in [14] as well as Theorem 2.2, we obtain the following oscillation criteria for (1).…”

“…In 2016, Karpuz andÖcalan [14] presented new sufficient conditions for the oscillation of first-order delay dynamic equation on time scales…”

Philos' inequality on time scales and its application in the oscillation theory

“…Some results for the asymptotic behaviour of solutions of higher-order dynamic equations can also be found in [2, 11, 12, 14-17, 20-22, 25, 28]. As we will be making comparison with first-order dynamic equations, we find useful to redirect the readers to the papers [4,5,7,9,10,19,23,26], where they can find the most important oscillation tests for first-order dynamic equations.…”

Oscillation criteria for first-order dynamic equations with nonmonotone delays

“…where c ∈ (0, 1) R , then every solution of equation ( 1.3) oscillates. Also, in 2016, Karpuz and Öcalan [19] enhanced the condition (1.7) by extending the second integral condition to the larger interval [τ (t), t] T as the following: Assume that τ (t) is eventually nondecreasing and…”