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2014 Oscillation Criteria of Even Order Delay Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals
Haidong Liu, Cuiqin Ma
Abstr. Appl. Anal. 2014: 1-8 (2014). DOI: 10.1155/2014/395381

Abstract

We study the oscillatory properties of the following even order delay dynamic equations with nonlinearities given by Riemann-Stieltjes integrals: (p(t)xΔn-1(t)α-1xΔn-1(t))Δ+f(t,x(δ(t))) + aσ(b)k(t,s)x(g(t,s))θ(s)sgn(x(g(t,s)))Δξ(s)=0, where t[t0,)𝕋:=[t0,)𝕋, 𝕋 a time scale which is unbounded above, n2 is even, f(t,u)q(t)uα, α>0 is a constant, and θ:[a,b]𝕋1 is a strictly increasing right-dense continuous function; p,q:[t0,)𝕋, k:[t0,)𝕋×[a,b]𝕋1, δ:[t0,)𝕋[t0,)𝕋, and g:[t0,)𝕋×[a,b]𝕋1[t0,)𝕋 are right-dense continuous functions; ξ:[a,b]𝕋1 is strictly increasing. Our results extend and supplement some known results in the literature.

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Haidong Liu. Cuiqin Ma. "Oscillation Criteria of Even Order Delay Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals." Abstr. Appl. Anal. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/395381

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022304
MathSciNet: MR3186963
Digital Object Identifier: 10.1155/2014/395381

Rights: Copyright © 2014 Hindawi

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