J Austral Math Soc Ser B 32 pp382--400, 1991.

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

L. H. Erbe, H. I. Freedman, X. Z. Liu and J. H. Wu

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 reaction-diffusion equation modeling the growth of a single-species population subject to abrupt changes of certain important system parameters.

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Authors

L. H. Erbe

Applied Mathematics Institute, University of Alberta, Edmonton, Canada T6G 2G1.

J. H. Wu

Applied Mathematics Institute, University of Alberta, Edmonton, Canada T6G 2G1.

X. Z. Liu

Applied Mathematics Institute, University of Alberta, Edmonton, Canada T6G 2G1.

Present address:

Department of Applied Mathematics, University of Waterloo, Waterloo, Canada.

H. I. Freedman

Applied Mathematics Institute, University of Alberta, Edmonton, Canada T6G 2G1.

Present address:

Department of Applied Mathematics, York University, North York, Canada.