Abstract
We will establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations on a time scale , where is a quotient of odd positive integers with , and real-valued positive rd-continuous functions defined on . To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study. Some examples are considered to illustrate the main results.
Highlights
The study of dynamic equations on time-scales, which goes back to its founder Hilger 1, is an area of mathematics that has recently received a lot of attention
It has been created in order to unify the study of differential and difference equations
Many results concerning differential equations carry over quite to corresponding results for difference equations, while other results seem to be completely different from their continuous counterparts
Summary
The study of dynamic equations on time-scales, which goes back to its founder Hilger 1 , is an area of mathematics that has recently received a lot of attention. To the best of our knowledge, there are no results regarding the oscillation of the solutions of the following third-order nonlinear neutral delay dynamic equations on timescales up to now: r t x t − atxτt ΔΔ Δ p t xγ δ t 0, t ∈ T.
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