Oscillation and comparison theorems for half-linear second-order difference equations

Oscillation Criteria for Second-Order Delay Dynamic Equations on Time Scales

“…Numerous oscillation and nonoscillation criteria have been established for the forms of (1.14) and (1.15); see, for example, [20][21][22][23][24][25][26] and references therein.…”

Oscillation criteria for half-linear dynamic equations on time scales

“…(1.3) when r(t) = 1 was studied by Thandapani et al [19] where γ > 0, p(t) is a positive sequence, and proved that every solution of (1…”

Kamenev-type oscillation criteria for second order nonlinear dynamic equations on time scales

“…Note that, also the oscillation of equation (3.6) when r(t) = 1 and f(t, x(g(t))) = p(t)x(t), was studied by Thandapani et al [28] where c > 0, p(t) is a positive sequence, and proved that every solution of (3.6) is oscillatory, if X 1 n¼n 0 pðnÞ ¼ 1: Similarly, we can state oscillation criteria for many other time scales, e.g., T ¼ hZ; h > 0; T ¼ N 2 0 :¼ fn 2 : n 2 N 0 g, or T ¼ fH n : n 2 Ng where H n is the so-called nth harmonic number defined by H 0 ¼ 0; H n ¼ P n k¼1 1 k ; n 2 N 0 .…”

“…Throughout this work a knowledge and understanding of time scales and time scale notation is assumed; for an excellent introduction to the calculus on time scales, see Bohner and Peterson [5,6]. In the last few years, there has been increasing interest in obtaining sufficient conditions for the oscillation/nonoscillation of solutions of different classes of dynamic equations on time scales, we refer the reader to the papers [3,4,7,11,13,17,[20][21][22][23][24][25][28][29][30][31][32], and the references cited therein.…”