Abstract
We employ Kranoselskii's fixed point theorem to establish the existence of nonoscillatory solutions to the second-order neutral delay dynamic equation on a time scale T. To dwell upon the importance of our results, one interesting example is also included.
Highlights
The theory of time scales, which has recently received a lot of attention, was introduced by Hilger in his Ph.D
For the notation used below we refer to the section that provides some basic facts on time scales extracted from Bohner and Peterson 3
There has been much research activity concerning the oscillation of solutions of various equations on time scales, and we refer the reader to Erbe 5, Saker 6, and Hassan 7
Summary
We employ Kranoselskii’s fixed point theorem to establish the existence of nonoscillatory solutions to the second-order neutral delay dynamic equation xtptx τ0 t ΔΔ q1 t x τ1 t − q2 t x τ2 t e t on a time scale T. To dwell upon the importance of our results, one interesting example is included.
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