DIFFUSIVE LOGISTIC EQUATIONS WITH TIME DELAY AND IMPULSES: EXISTENCE OF SOLUTION AND ATTRACTORS

Abstract

A diffusive logistic equation with impulses and single time delay, with zero Robin boundary condition and Holder continuous initial function is studied. The impulses which are continuous functions, occur at fixed times. The magnitude of delay is equal to or less than the difference of any two successive impulse times. The method of upperand lower solution is used for finding the solution. The sufficient conditions for the zero solution to be an attractor of this system is presented. In the case of Neumann boundary condition, existence of positive attractor is proved under certain conditions.

DOI : http://dx.doi.org/10.22342/jims.13.1.75.61-72