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

J. Widjaja; M.J. Bottema

doi:10.22342/jims.13.1.75.61-72

J. Widjaja ⁽¹⁾ , M.J. Bottema ⁽²⁾

(1) Analysis and Geometry Group, FMIPA, Institut Teknologi Bandung, Jl. Ganesa 10 Ban- dung 40132, Indonesia., Indonesia,

(2) School of Informatics and Engineering, Flinders University, GPO Box 2100 SA 5001, Australia., Australia

https://doi.org/10.22342/jims.13.1.75.61-72

Issue
Volume 13 Number 1 (April 2007)

Submitted
May 25, 2012

Accepted
July 1, 2012

Published
July 1, 2012

Keywords:

delay, impulse, logistic, diffusion

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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

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Authors

J. Widjaja

Analysis and Geometry Group, FMIPA, Institut Teknologi Bandung, Jl. Ganesa 10 Ban- dung 40132, Indonesia.

penulis@jims-a.org (Primary Contact)

M.J. Bottema

School of Informatics and Engineering, Flinders University, GPO Box 2100 SA 5001, Australia.

Widjaja, J., & Bottema, M. (2012). DIFFUSIVE LOGISTIC EQUATIONS WITH TIME DELAY AND IMPULSES: EXISTENCE OF SOLUTION AND ATTRACTORS. Journal of the Indonesian Mathematical Society, 13(1), 61–72. https://doi.org/10.22342/jims.13.1.75.61-72