Forced Oscillation of Nonlinear Impulsive Hyperbolic Partial Differential Equation with Several Delays

Abstract

In this paper, we study oscillatory properties of solutions for the nonlinear impulsive hyperbolic equations with several delays. We establish sufficient conditions for oscillation of all solutions.

On The Oscillation of Impulsive Neutral Partial Differential Equations with Distributed Deviating Arguments and Damping Term

“…This paper generalizes many results of hyperbolic partial differential equations without impulse and distributed deviating arguments. Many authors studied the oscillation of partial differential equations with or wihtout impulse, see [15,16,14,12,26,20] and the references cited therein. While comparing the importance between impulsive differential equations and corresponding differential equations, impulsive type has wide applications in various fields of science and technology.…”

“…Theorem 4.1 If the impulsive functional differential inequality 16) has no eventually positive solution, then every solution of the boundary value problem defined by (E) and (B2) is oscillatory in G. Proof: Suppose to the contrary that u(x, t) = 0 is solution of the boundary value problem (E), (B2). Which has a constant sign in the domain Ω × [t 0 , +∞).…”

Oscillation of Even Order Impulsive Neutral Partial Differential Equations with Distributed Deviating Arguments

“…Impulsive ordinary and partial functional differential equations have wide range of applications in a variety of fields of science and machinery [1,8,18,24]. The oscillation of impulsive and non-impulsive parabolic and hyperbolic equations has been widely studied in the literature [13,15,16,17,20,21,25]. Curiously very few significant consequences on higher order partial differential equations with continuous distributed deviating ISSN: 2456-8686, Volume 1, Issue 1, 2017:37-60 DOI : http://doi.org/10.26524/cm3…”

On the Oscillation of Impulsive Vector Partial Differential Equations with Damping Term

“…The first paper on impulsive partial differential equations [3] was published in 1991. Following these early results, several authors worked on the oscillatory behavior of impulsive partial differential equations with delays [4,9,10,11,26,17,18,19,20,21] ISSN: 2456-8686, Volume 1, Issue 2, 2017:91-112 DOI : http://doi.org/10.26524/cm19…”