Forced oscillation of second-order half-linear dynamic equations on time scales
Summary: We establish a new interval oscillation criterion for the second-order half-linear dynamic equation \[ (r(t)[x^\Delta(t)]^\alpha)^\Delta+p(t)x^\alpha(\sigma(t))=f(t) \] on a time scale \(\mathbb T\) which is unbounded. This criterion is an extension of the oscillation result for second order linear dynamic equation established by \textit{L. Erbe, A. Peterson} and \textit{S. H. Saker} [J. Difference Equ. Appl. 14, No.~10--11, 997--1009 (2008; Zbl 1168.34025)]. As an application, we obtain a sufficient condition for oscillation of the second-order half-linear differential equation \[ ([x'(t)]^\alpha)'+c\sin tx^\alpha(t)=\cos t, \] where \(\alpha=p/q\), \(p, q\) are odd positive integers.
scientific article; zbMATH DE number 5791615