New oscillation criteria for second-order neutral dynamic equations on time scales via Riccati substitution

作者：Saker S H^*; O' Regan Donal

来源：Hiroshima Mathematical Journal, 2012, 42(1): 77-98.

• Oscillation
• second-order neutral dynamic equation
• time scales

In this paper, we consider the second-order nonlinear neutral functional dynamic equation %26lt;br%26gt;(p(t)([y(t) + r(t)y(tau(t))](Delta))(gamma))(Delta) + f(t,y(delta(t))) = 0, %26lt;br%26gt;on a time scale T and establish some new sufficient conditions for oscillation. Our results improve oscillation results for neutral delay dynamic equations on time scales and are new when delta(t) %26gt; t and/or 0 %26lt; gamma %26lt; 1. Furthermore our results can be applied on the time scales T = hT, for h %26gt; 0, T = q(N) = {t : t = q(k)}, k is an element of N, q %26gt; 1, T = N-2 = {t(2) : t is an element of N}, T-2 = {root n : n is an element of N-0}, T3 = {(3)root n : n is an element of N-0}, and when T = Tn = {t(n) : n is an element of N-0} where {tn} is the set of harmonic numbers, etc.

• 出版日期2012-3