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Comparison principles for impulsive parabolic equations with applications to models of single species growth. (English) Zbl 0881.35006
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.

MSC:
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
92D25 Population dynamics (general)
35B50 Maximum principles in context of PDEs
35K57 Reaction-diffusion equations
34A37 Ordinary differential equations with impulses
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