This paper is devoted to studying the asymptotic stability of retarded nonlinear functional differential equations by the method of Lyapunov functionals. Under the as-sumption that there exists a positive definite tim...This paper is devoted to studying the asymptotic stability of retarded nonlinear functional differential equations by the method of Lyapunov functionals. Under the as-sumption that there exists a positive definite time-invariant Lyapunov functional with negative semi-definite derivative, we focus on the extra conditions to guarantee the asymptotic stability, and present a new criterion, which is less conservative than the classical one. Finally, an example is given to illustrate the effectiveness of the result.展开更多
In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s p...In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s periodic solution theorem. Anexample of application is given at the end.展开更多
In this paper, some kinds of Liapunov functionals are constructed. By these constructions we have obtained some criteria for the uniform asymptotic stability of zero solution of several RFDE systems. These criteria ar...In this paper, some kinds of Liapunov functionals are constructed. By these constructions we have obtained some criteria for the uniform asymptotic stability of zero solution of several RFDE systems. These criteria are in concise forms, easily checked and applicable.展开更多
This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established...This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established by combining the theory of monotone semiflows generated by RFDEs with infinite delay and the fixed point theorems of solution operators. A nontrivial application of the results obtained here to a well-known nonautonomous Lotka-Volterra system with infinite delay is also presented.展开更多
基金supported by the National Basic Research Program of China (973 Program,Grant No.2005CB321902)the National Natural Science Foundation of China (Grant No.60473109+1 种基金No.60374001)the Doctor Fund of Ministry of Education of China (No.20030006003)
文摘This paper is devoted to studying the asymptotic stability of retarded nonlinear functional differential equations by the method of Lyapunov functionals. Under the as-sumption that there exists a positive definite time-invariant Lyapunov functional with negative semi-definite derivative, we focus on the extra conditions to guarantee the asymptotic stability, and present a new criterion, which is less conservative than the classical one. Finally, an example is given to illustrate the effectiveness of the result.
文摘In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s periodic solution theorem. Anexample of application is given at the end.
文摘In this paper, some kinds of Liapunov functionals are constructed. By these constructions we have obtained some criteria for the uniform asymptotic stability of zero solution of several RFDE systems. These criteria are in concise forms, easily checked and applicable.
基金Project supported by NNSF of China (No:19971026).
文摘This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established by combining the theory of monotone semiflows generated by RFDEs with infinite delay and the fixed point theorems of solution operators. A nontrivial application of the results obtained here to a well-known nonautonomous Lotka-Volterra system with infinite delay is also presented.
