New interval oscillation criteria for second-order functional differential equations with nonlinear damping

Abstract

This paper concerns the oscillation problem of second-order nonlinear damped ODE with functional terms.We give some new interval oscillation criteria which is not only based on constructing a lower solution of a Riccati type equation but also based on constructing an upper solution for corresponding Riccati type equation. We use a recently developed pointwise comparison principle between those lower and upper solutions to obtain our results. Some illustrative examples are also provided to demonstrate our results.

Oscillatory behavior of solutions of certain fractional difference equations

“…Many authors have been focused on various equations like ordinary and partial differential equations [3][4][5][6], difference equations [7][8][9], dynamic equations on time scales [10][11][12][13][14], and fractional differential (difference) equations [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] obtaining some oscillation criteria. Recently, oscillation studies have become a very hot topic.…”