Asymptotic Behavior Of Solutions Of Periodic Competition Diffusion System With Depositings

In this paper, we study the asymptotic behavior of the solution of periodic competition diffusion system with depositingswith the initial conditionsby using upper-lower-solution method and the basic parabolic estimates and the parabolic maximum principle, where ? is a smooth bounded region in h, k are all positive constants, are all functions in space satisfyingthat Our main results are stated as follows:(i) If DI, D2, a, b, c, d, e, /are all positive constants, then there exists a unique positive constant equilibrium solution (u , v) of system (1) (2), and for arbitrarilly given initial functions p(x), y/(x) satisfying the above conditions the unique solution (u(x, f), v(jc, /)) of problem (1)-(3) satisfies thatuniformly with respect to x in fi.(ii) If D 2, a, b, c, c/, e, /which belong to space are all strictly positive and 7-periodic in on then there exist two strictly positiveT- periodic solutions of system (1^ (2) denoted by and t)), and for arbitrarilly given initial functions satisfying the above conditions the unique solution (u(x, 1), v(x, ) of problem (1)-(3) satisfies that for given there exists such that when,uniformly with respect to x in.(iii) If are stated as in section (ii) and a, b, c, d, e,/which belong to space are all strictly positive and asymptotically 7- periodic in, then thereexist two strictly positive T- periodic solutions of the limit system of system (1) (2) which are denoted by and , and for arbitrarilly given initial functions satisfying the above conditions the unique solution of problem (l)-(3) satisfies that for given there exists such that when .uniformly with respect to x in .The results in this paper may be viewed as the extention of the main results of [3, 4, 5, 6].