Asymptotic behaviour of solutions of periodic competition diffusion system

On the Nonautonomous Volterra-Lotka Competition Equations

“…We wish to point out that the main result in this paper and some of the methods used have been motived by [3]. Also, Zhou and Pao [8] established a somewhat similar result for a system of reaction-diffusion equations where the coefficients were assumed to be positive constants.…”

“…Suppose that v > 0. In order to obtain a contradiction, we first establish the inequality (3) aL < bMu + cMv.…”

“…The periodic case was studied in [4]. A similar system, involving reaction-diffusion equations, with periodic coefficients was studied in [3]. For the ecological significance of the system (*), the reader is referred to [7] and the works cited above.…”

Persistence in a Periodic Competitor-Competitor-Mutualist Diffusion System

“…When a 3 = 0, the system (1.1) reduces to the classical LotkaVolterra competition model which has been investigated by many authors (see [1,8]). …”

“…In this paper, following some ideas of Ahmad and Lazer [1], we study the asymptotic behavior of solutions of system (1.1)-(1.3). We shall prove that under certain conditions this system is persistent and under some other conditions it exhibits extinction or, more exactly, the species of mutualist extincts.…”