Abstract
Under a couple of canonical and mixed canonical-noncanonical conditions, we investigate the oscillation and asymptotic behavior of solutions to a class of third-order nonlinear neutral dynamic equations with mixed deviating arguments on time scales. By means of the double Riccati transformation and the inequality technique, new oscillation criteria are established, which improve and generalize related results in the literature. Several examples are given to illustrate the main results.
Highlights
The theory of time scales provides a powerful tool for unifying and extending the knowledge about continuous and discrete systems, which has attracted the attention of many scholars in recent years, see the monographs [1,2] for the essentials about the subject
The research on the oscillation and asymptotic behavior of solutions to different types of differential equations and dynamic equations has been a topic of interest in the past two decades, see, for instance, Refs. [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32] and the references cited therein
In this paper, we are concerned with the oscillation and the asymptotic behavior of solutions to third-order nonlinear neutral functional dynamic equations with mixed deviating arguments of the form (b(t)(( a(t)(z(t))∆ )∆ )α )∆ + f (t, x (δ(t))) = 0, t ∈ [t0, ∞)T
Summary
The theory of time scales provides a powerful tool for unifying and extending the knowledge about continuous and discrete systems, which has attracted the attention of many scholars in recent years, see the monographs [1,2] for the essentials about the subject. A majority of the related research (e.g., the results from references stated in (i)–(viii)) were given under the double canonical condition.
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