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

Raegan Higgins

doi:10.3934/dcdsb.2010.13.609

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2010, Volume 13, Issue 3: 609-622. Doi: 10.3934/dcdsb.2010.13.609

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

Raegan Higgins^1,

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

Received: May 31, 2009

Revised: December 31, 2009

Published: September 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 34K11, 39A10; Secondary: 39A99.

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