Comparison principles for impulsive parabolic equations with applications to models of single species growth

Abstract

This paper establishes some maximum and comparison principles relative to lower and upper solutions of nonlinear parabolic partial differential equations with impulsive effects. These principles are applied to obtain some sufficient conditions for the global asymptotic stability of a unique positive equilibrium in a reactiondiffusion equation modeling the growth of a single-species population subject to abrupt changes of certain important system parameters.

Oscillation of Neutral Nonlinear Impulsive Parabolic Equations with Continuous Distributed Deviating Arguments

“…In 1991, the first paper [6] on this class of equations was published. However, we only find a few of papers on oscillation theory of impulsive partial differential equations.…”

Impulsive control and synchronization of spatiotemporal chaos

“…., m 1 , then there exists a local solution u(t, x) for system (1) satisfying qðtÞ 6 uðt; xÞ 6 cðtÞ provided that the original partial differential equation, in (1), without the impulses, has a solution [7]. For…”

Upper and Lower Solutions Method for Impulsive Differential Inclusions With Nonlinear Boundary Conditions

“…The theory of impulsive differential equations or inclusions has become an active area of investigation due to their applications in the fields of mechanics, electrical engineering, medicine biology, ecology, and so on, see [5,6,12,18]. Critical point theory plays a major role in discussing the existence of solutions for boundary problem for impulsive differential inclusions, see [9,10,11,16,17].…”