Oscillation Criteria for Functional Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integral-Reference-Cited by-同舟云学术

Oscillation Criteria for Functional Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integral

Published:2014 Issue: Volume:2014 Page:1-9
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Sun Yuangong¹,Hassan Taher S.²³

Affiliation:

1. School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China

2. Department of Mathematics, Faculty of Science, University of Hail, Hail 2440, Saudi Arabia

3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Abstract

We present new oscillation criteria for the second order nonlinear dynamic equation[r(t)ϕγ(xΔ(t))]Δ+q0(t)ϕγ(x(g0(t)))+∫ab‍q(t,s)ϕα(s)(x(g(t,s)))Δζ(s)=0under mild assumptions. Our results generalize and improve some known results for oscillation of second order nonlinear dynamic equations. Several examples are worked out to illustrate the main results.

Funder

Natural Science Foundation of Shandong Province

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/697526.pdf

Reference28 articles.

1. Quantum Calculus

2. Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus

3. Dynamic Equations on Time Scales