Oscillation criteria for a class of second-order Emden–Fowler delay dynamic equations on time scales☆

By Zhenlai Han, Shurong Sun, B. Shi. 2007

90 citations recorded by the source corpus.

Abstract By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden–Fowler delay dynamic equations x Δ Δ ( t ) + p ( t ) x γ ( τ ( t ) ) = 0 on a time scale T ; here γ is a quotient of odd positive integers with p ( t ) real-valued positive rd-continuous functions defined on T . To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales. Our results in this paper not only extend the results given in [R.P. Agarwal, M. Bohner, S.H. Saker, Oscillation of second-order delay dynamic equations, Can. Appl. Math. Q. 13 (1) (2005) 1–18] but also unify the oscillation of the second-order Emden–Fowler delay differential equation and the second-order Emden–Fowler delay difference equation.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2f2f7352988b3f5ebd0b722af73872ff42b204d7

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In Applied Mathematics

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Citations in the corpus

Oscillation of second-order delay dynamic equations on time scales (2009, unknown): “Han [ 10 ] investigated the second-order Emden-Fowler delay dynamic equations on time scales x �� (t) + p(t)x γ (τ (t)) = 0 ,t ∈ T, (1.7)”
A numerical approach for solving a class of variable-order fractional functional integral equations (2018, background): “Recently, there has been an increasing attention in considering the oscillatory behavior of the Emden–Fowler functional dynamic equations and their generalization because of the application to gaseous dynamics in astrophysics (Han et al. 2007; Chen 2010; Li et al. 2011; Liu et al. 2012; Thandapani a”
Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations (2009, methodology): “In [18], the authors considered the second-order Emden–Fowler dynamic equation on time scales xDD þ qðtÞxa 1⁄4 0, where a is the ratio of odd integers, and they used the Riccati transformation technique to obtain several oscillation criteria for this equation.”