Oscillation of second order differential equations with mixed nonlinearities

Abstract

By refining the standard integral averaging technique, in this paper, new oscillation criteria as well as interval oscillation criteria are established for the second order delay differential equation with mixed nonlinearitieswhere α > 0 , αi > 0, i = 1, 2, · · · , n . Our results generalize and improve the known results in the literature. Examples are also given to illustrate the importance of our results.

On the oscillation of higher order fractional difference equations with mixed nonlinearities

“…Such equations often arise in the growth of bacterial populations with competitive species [5]. Several techniques such as Riccati transformation, mathematical inequalities, principle solution and integral averaging method have been employed to establish sufficient conditions for the oscillation of these types of equations [6,7,8,9,10,11].…”