Oscillation of even order advanced type dynamic equations with mixed nonlinearities on time scales

Oscillation of third order nonlinear damped dynamic equation with mixed arguments on time scales

“…In recent years, there has been an increasing interest in studying the oscillation of solutions of the equations, we refer the readers to [1][2][3][4][5][6][7][8][9][10][11][12][13] and the references cited therein. The dynamic equations with deviating arguments are deemed to be adequate in modeling of the countless processes in all areas of science.…”

“…And there are many results on the oscillation of the delay dynamic equation, we refer the readers to [4][5][6][7][8][10][11][12][13] and the references cited therein. The study of dynamic equation with mixed arguments is also of great significance, due to the comprehensive use in natural science and theoretical study.…”

“…Thus, our method essentially simplifies the examination of the third order equation; and what is more, it supports backward the research on the second order advanced dynamic equation. For the study of oscillation of the advanced equation, we refer the readers to [3,9,10]. Indeed, there are no known results about the oscillation of the third order damped advanced dynamic equation in the form of (1.1) when q(t) ≡ 0.…”

Oscillation Criteria of Even Order Delay Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals

“…In recent years, more and more people have been interested in studying the oscillatory behavior of higher order dynamic equations on time scales, see [1][2][3][4][5][6][7][8][9][10][11][12][13] and references therein. For an introduction to time scale calculus and dynamic equations, we refer the reader to the landmark paper of Hilger [14] and the seminal book by Bohner and Peterson [15] for a comprehensive treatment of the subject.…”

“…By employing generalized Riccati techniques, he established some new criteria which ensure that (2) is oscillatory. Chen and Qu [8] investigated the even order advanced type dynamic equation (3). They got some new oscillation criteria for (3) by introducing parameter functions.…”