Asymptotic behavior of solutions of second order nonlinear dynamic equations. (English) Zbl 1314.34180
Summary: This paper is concerned with the asymptotic behavior of solutions of second order nonlinear dynamic equation
\[
(r(t) x^\Delta(t))^\Delta+ p(t) \phi_\gamma(x(t))= 0,
\]
on an above-unbounded time scale \(\mathbb{T}\) where \(\gamma\) is a positive constant and where, in addition, \(r\) and \(p\) are real-valued, rd-continuous functions on \(\mathbb{T}\) with no explicit sign assumptions on \(p\). Our results are established for a time scale \(\mathbb{T}\) without assuming certain restrictive conditions on \(\mathbb{T}\). Several examples illustrating our results will be given.
MSC:
34N05 | Dynamic equations on time scales or measure chains |
34D05 | Asymptotic properties of solutions to ordinary differential equations |