Abstract
In this paper, we will study the oscillatory properties of the second order half-linear dynamic equations with distributed deviating arguments on time scales. We obtain several new sufficient conditions for the oscillation of all solutions of this equation. Our results not only unify the oscillation of second order nonlinear differential and difference equations but also can be applied to different types of time scales with sup T = ∞. Our results improve and extend some known results in the literature. Examples which dwell upon the importance of our results are also included.
Highlights
In this paper, we are concerned with the oscillatory behavior of solutions of second-order half-linear neutral type dynamic equation with distributed deviating arguments of the form r (t )ψ ( x )) ) + p −τ ))∆ α
Our results unify the oscillation of second order nonlinear differential and difference equations and can be applied to different types of time scales with sup = ∞
We are concerned with the oscillatory behavior of solutions of second-order half-linear neutral type dynamic equation with distributed deviating arguments of the form
Summary
We are concerned with the oscillatory behavior of solutions of second-order half-linear neutral type dynamic equation with distributed deviating arguments of the form [1] Bohner et al proved several theorems provided sufficient conditions for oscillation of all solutions of the second order Emden-Fowler dynamic equations of the form ( p (t ) x∆ (t ))∆ + q (t ) xγ (σ (t )) = 0.
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