Oscillation criteria for second-order nonlinear delay dynamic equations

Abstract

In this paper, we consider the second-order nonlinear delay dynamic equationon a time scale T. By employing the generalized Riccati technique we will establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. The obtained results improve the well-known oscillation results for dynamic equations and include as special cases the oscillation results for differential equations. Some applications and examples are considered to illustrate the main results.

Oscillation criteria for quasi-linear functional dynamic equations on time scales

“…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. For contribution, we refer the reader to the papers [1,2,3,4,5,6,7,8,9,12,13,14,15,16,18,19,20,21,28,29,30,31,32,33,34], and the references cited therein.…”

New Oscillation Criteria of Second-Order Nonlinear Delay Dynamic Equations on Time Scales

“…In 2007, Erbe, Peterson and Saker [3] considered the general nonlinear delay dynamic equations (4) and obtained some new oscillation criteria, which improved the results given by Sahiner [2]. Saker [4] in 2005 and Grace, Bohner and Agarwal [5] in 2009 considered the half-linear dynamic equations (5), and established some sufficient conditions for oscillation of (5).…”

Oscillation criteria for nonlinear neutral functional dynamic equations on time scales

“…In recent years there has been a great deal of research activity concerning the oscillation and nonoscillation of solutions of second order dynamic equations on time scales, we refer the reader to the papers [1,2,[5][6][7]10,11,[14][15][16][17][18][31][32][33]35,36,39] and the references cited therein. For oscillation of neutral dynamic equations we refer the reader to the papers [3,27,34,37,38,43] and for oscillation of different types of equations we refer the reader to the book by the second author [30].…”