A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are pr...A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are presented about p-moment boundedness in the process by Liapunov method with nonlinear item dependent on the impulsive effects, which may gain wider use in industrial engineering, physics, etc. At last, an example is given to show an theoretical application of the obtained results.展开更多
We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
In this paper, by means of Liapunov functionals, we establish the criteria of uniform boundedness and uniform ultimate boundedness for infinite delay difference systems in terms of two measures. Moreover, an example i...In this paper, by means of Liapunov functionals, we establish the criteria of uniform boundedness and uniform ultimate boundedness for infinite delay difference systems in terms of two measures. Moreover, an example is given to illustrate the obtained results.展开更多
We study a system(D)x’=F(t,x_t)of functional differential equations,together with a scalar equation(S)x’=-a(t)f(x)+b(t)g(x(t-h))as well as perturbed forms.A Liapunov functional is constructed which has a derivative ...We study a system(D)x’=F(t,x_t)of functional differential equations,together with a scalar equation(S)x’=-a(t)f(x)+b(t)g(x(t-h))as well as perturbed forms.A Liapunov functional is constructed which has a derivative of a nature that has been widely discussed in the literature. On the basis of this example we prove results for(D)on asymptotic stability and equi-boundedness.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
In this paper, the boundedness and the stability of solutions for a class of fourth order nonlinear differential equations are studied by using the method of Liapunov function. The sufficient conditions which guarante...In this paper, the boundedness and the stability of solutions for a class of fourth order nonlinear differential equations are studied by using the method of Liapunov function. The sufficient conditions which guarantee the boundedness and stability of solutions are preasented.展开更多
This paper considers a class of p-NFDEs. By Liapunov functionals, we establish two boundedness criteria, which improve some boundedness conditions for FDEs in the literature. Some examples are also worked out to demon...This paper considers a class of p-NFDEs. By Liapunov functionals, we establish two boundedness criteria, which improve some boundedness conditions for FDEs in the literature. Some examples are also worked out to demonstrate the advantages of our results.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
基金The Special Research Funds for Young Col-lege Teacher of Shanghai (No. 355877)
文摘A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are presented about p-moment boundedness in the process by Liapunov method with nonlinear item dependent on the impulsive effects, which may gain wider use in industrial engineering, physics, etc. At last, an example is given to show an theoretical application of the obtained results.
文摘We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
文摘In this paper, by means of Liapunov functionals, we establish the criteria of uniform boundedness and uniform ultimate boundedness for infinite delay difference systems in terms of two measures. Moreover, an example is given to illustrate the obtained results.
基金Supported in part by NSF of China,Key Project # 19331060
文摘We study a system(D)x’=F(t,x_t)of functional differential equations,together with a scalar equation(S)x’=-a(t)f(x)+b(t)g(x(t-h))as well as perturbed forms.A Liapunov functional is constructed which has a derivative of a nature that has been widely discussed in the literature. On the basis of this example we prove results for(D)on asymptotic stability and equi-boundedness.
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The Applied Foundation of the Education Department of Yunnan Province(0012226)
文摘In this paper, the boundedness and the stability of solutions for a class of fourth order nonlinear differential equations are studied by using the method of Liapunov function. The sufficient conditions which guarantee the boundedness and stability of solutions are preasented.
文摘This paper considers a class of p-NFDEs. By Liapunov functionals, we establish two boundedness criteria, which improve some boundedness conditions for FDEs in the literature. Some examples are also worked out to demonstrate the advantages of our results.
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.
