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

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Abstract

In this paper, we consider the second-order nonlinear dynamic equation (p(t)yΔA(t)Δ + f(t, yσ)g(p(t) Δ) = 0, on a time scale 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.

Original languageEnglish
Pages (from-to)609-622
Number of pages14
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume13
Issue number3
DOIs
StatePublished - May 2010

Keywords

  • Asymptotic behavior
  • Dynamic equations
  • Lower solutions
  • Time scale
  • Upper solutions

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