American Institute of Mathematical Sciences

May  2010, 13(3): 609-622. doi: 10.3934/dcdsb.2010.13.609

Asymptotic behavior of second-order nonlinear dynamic equations on time scales

 1 Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States

Received  June 2009 Revised  January 2010 Published  February 2010

In this paper, we consider the second-order nonlinear dynamic equation

$(p(t)y^{\Delta}(t))^{\Delta}+f(t, y^{\sigma})g(p(t)y^{\Delta})=0,$

on a time scale $\mathbb{T}$. Our goal is to establish necessary and sufficient conditions for the existence of certain types of solutions of this dynamic equation. We apply results from the theory of lower and upper solutions for related dynamic equations and use several results from calculus.

Citation: Raegan Higgins. Asymptotic behavior of second-order nonlinear dynamic equations on time scales. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 609-622. doi: 10.3934/dcdsb.2010.13.609
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