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http://dx.doi.org/10.14317/jami.2012.30.1_2.219

ON THE OSCILLATION OF SECOND-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES

Zhang, Quanxin (Department of Mathematics and Information Science, Binzhou University)
Sogn, Xia (Department of Mathematics and Information Science, Binzhou University)
Gao, Li (Department of Mathematics and Information Science, Binzhou University)

Publication Information

Journal of applied mathematics & informatics / v.30, no.1_2, 2012 , pp. 219-234 More about this Journal

Abstract

By using the generalized Riccati transformation and the inequality technique, we establish some new oscillation criterion for the second-order nonlinear delay dynamic equations $(a(t)(x^{\Delta}(t))^{\gamma})^{\Delta}+q(t)f(x({\tau}(t)))=0$ on a time scale $\mathbb{T}$ , here ${\gamma}{\geq}1$ is the ratio of two positive odd integers with $a$ and $q$ real-valued positive right-dense continuous functions defined on $\mathbb{T}$ . Our results not only extend and improve some known results, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation.

Keywords

oscillation criterion; dynamic equations; time scale;

Citations & Related Records

Reference

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