By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and constructing Lyapunov functionals,a set of easily verifiable sufficient conditions are derived for the existence and global attractivity of a positive periodic solution to a predator-prey system with delays and impulses.
Ren Yaping(School of Statistic and Math.,Yunnan University of Finance and Economics,Kunming 650221) Li Yongkun(Dept. of Math.,Yunnan University,Kunming 650091)
By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f（n,x（n-τ1（n））,…,x（n-τm（n））,u（n-δ（n）））,△u（n）=-η（n）u（n）＋a（n）x（n-σ（n））,n∈Z.
By using Krasnoselskii’s fixed-point theorem on a suitable cone, several existence results and corresponding properties of positive solutions of nonlocal boundary value problem for nonlinear retarded differential equation are obtained. MR Subject Classification 34K10 Keywords positive solution - retarded differential equation - nonlocal boundary value problem - Krasnoselskii’s fixed-point theorem Supported by the National Natural Science Foundation of China (10361006), the Natural Science Foundation of Yunnan Province (2003A0001M), Youth Natural Science Foundation of Yunnan Univ. (K1059099) and Science Foundation of Yunnan Educational Community.
