Interval oscillation criteria for second-order forced impulsive delay differential equations with damping term

Abstract

In this paper, we present some sufficient conditions for the oscillation of all solutions of a second order forced impulsive delay differential equation with damping term. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. The results obtained in this paper extend and generalize some of the the known results for forced impulsive differential equations. An example is provided to illustrate the main result.

Interval Oscillation Criteria for Second-Order Impulsive Delay Differential Equations With Mixed Nonlinearities V. Muthulakshmi and R. Manjuram

“…In recent years, a great deal of effort has been spent in getting sufficient conditions for the oscillation of solutions of second order nonlinear impulsive delay differential equations. Recently, interval oscillation of impulsive delay differential equations was attracting the interest of many researchers, see [6,7,12,15,16,20,21,22]. However, for the impulsive equations, almost all of interval oscillation results in the existing literature were established only for the case of "constant delay ".…”

Interval oscillation criteria for impulsive conformable fractional differential equations

“…In the last decades, interval oscillation of impulsive di¤erential equations was arousing the interest of many researchers, see [7,8,11,15,16,19,20,21,23,25] and the references cited therein. Most of the existing literature concentrated on interval oscillation criteria for case of without delay and only very few papers appeared for case of with delay.…”

Forced oscillation of conformable fractional partial delay differential equations with impulses

“…The study of the qualitative behavior of partial differential equations has rapidly expanded in the last few decades, see for example [11,14,15,24,25,26,29,30,32] and the references they are cited. In particular, the problem of interval oscillation criteria for integer and fractional order impulsive differential equations have been investigated by few authors, we refer the reader to [3,4,19,28,31] and the references cited therein.…”