On the oscillation of impulsive vector partial differential equations with distributed deviating arguments

Abstract

In this paper, we consider a class of nonlinear impulsive neutral partial functional differential equations with continuous distributed deviating arguments. For this class, we establish sufficient conditions for the H-oscillation of the solutions, using impulsive differential inequalities and an averaging technique with two different boundary conditions. We provide an example to illustrate the main result.

On the Oscillation of Conformable Impulsive Vector Partial Differential Equations

“…On the other hand, it is easy to see that u H (x, t) satisfies the boundary condition(9). This is a contradiction to the hypothesis.Similarly, if u H (x, t) is eventually negative, using Lemma 2.1, we easily obtain that u H (x, t) satisfies the scalar impulsive partial differential inequality(4). It is obvious that u H (x, t) satisfies the boundary condition(9).…”

“…Several authors worked on the oscillatory behaviour of impulsive partial differential equations with delays [11,14,21,23,28]. For the essential background on the oscillation theory of differential equations, we refer the reader to the monographs [17,32,33] and the references cited therein [3,5,9,22].…”

“…We refer the reader to [8,20,24,25] for the background in the oscillation of vector differential equations. However, there are only a few papers [4,19,27] dealing impulsive vector partial differential equations.…”

Oscillation criteria for fractional impulsive hybrid partial differential equations

“…Its consequences were included in the book [15]. Chatzarakis et al [3], Kalaimani et al [13], Prakash et al [20], Sadhasivam et al [23,25] and Yang et al [30] studied the impulsive partial differential equations. The study of impulsive partial differential equations is motivated by various applications in population models [2], single species growth [6], feedback control prey-predator model [12], and various scientific models [29,31].…”