Abstract
In this paper, we make a detailed analysis of the structure of non-oscillatory solutions for second order superlinear and sublinear dynamic equations on time scales. The sufficient and necessary conditions for existence of non-oscillatory solutions are presented.
Highlights
During the past few decades, an active worldwide research on the oscillation and nonoscillation for dynamic equations on time scales has been carried out by many mathematicians
For some recent results on the topic, we refer the reader to the works [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] and the references cited therein
To the authors’ knowledge, there are no papers dealing with the analysis of structure of non-oscillatory solutions and sufficient and necessary conditions for existence of all kinds of non-oscillatory solutions for dynamic equations on time scales
Summary
During the past few decades, an active worldwide research on the oscillation and nonoscillation for dynamic equations on time scales has been carried out by many mathematicians. Many researchers have studied oscillation of second order dynamic equations. For some recent results on the topic, we refer the reader to the works [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] and the references cited therein. Consider the second order dynamic equation on time scales [ p(t) x ∆ (t)]∆ + g(t, x (η (t))) = 0, t ∈ T0 ⊆ T,.
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