本文讨论了一类具有无穷时滞的泛函微分方程N′(t)=-a(t)N(t)+b(t)integral from n=0 to∞(K(s)e^(-q(t)N(t-s)))ds,t(?)0,(*)正概周期解的存在唯一性和全局吸引性问题,利用锥中不动点定理,不仅得到了上述系统的正概周期解的存在唯一性...本文讨论了一类具有无穷时滞的泛函微分方程N′(t)=-a(t)N(t)+b(t)integral from n=0 to∞(K(s)e^(-q(t)N(t-s)))ds,t(?)0,(*)正概周期解的存在唯一性和全局吸引性问题,利用锥中不动点定理,不仅得到了上述系统的正概周期解的存在唯一性和全局吸引性的结论,还改进了文献[15]的主要结果,并且我们的方法比压缩映象原理要好.如果(*)中所有的系数都为周期的,相应的结论也是成立的,此时,我们的结果也推广了现有文献的结论.展开更多
In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost period...In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived.展开更多
文摘本文讨论了一类具有无穷时滞的泛函微分方程N′(t)=-a(t)N(t)+b(t)integral from n=0 to∞(K(s)e^(-q(t)N(t-s)))ds,t(?)0,(*)正概周期解的存在唯一性和全局吸引性问题,利用锥中不动点定理,不仅得到了上述系统的正概周期解的存在唯一性和全局吸引性的结论,还改进了文献[15]的主要结果,并且我们的方法比压缩映象原理要好.如果(*)中所有的系数都为周期的,相应的结论也是成立的,此时,我们的结果也推广了现有文献的结论.
基金Supported by the NNSF of China(11171135)Supported by the Jiangsu Province Innovation Project of Graduate Education(1221190037)
文摘In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived.
基金Supported by the National Natural Science Foundation of China(11071001)the Key Project of Anhui Provincial Education Department(KJZ2009A2005z)the Research Fund for the Doctoral Program of Higher Education of China(20093401110001)
