Open AccessOscillatory behaviour of higher-order nonlinear neutral delay dynamic equations on time scales
Author(s) -
M. M. A. El-Sheikh,
Mohamed Abdalla,
A.M. Hassan
Publication year - 2018
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1807635e
Subject(s) - mathematics , quotient , dynamic equation , oscillation (cell signaling) , order (exchange) , integer (computer science) , nonlinear system , combinatorics , pure mathematics , mathematical analysis , discrete mathematics , physics , quantum mechanics , computer science , economics , finance , biology , genetics , programming language
In this paper, new sufficient conditions are established for the oscillation of solutions of the higher order dynamic equations [r(t)(z?n-1(t))?]? + q(t) f(x(?(t)))=0, for t ?[t0,?)T, where z(t):= x(t)+ p(t)x(?(t)), n ? 2 is an even integer and ? ? 1 is a quotient of odd positive integers. Under less restrictive assumptions for the neutral coefficient, we employ new comparison theorems and Generalized Riccati technique.