By means of the properties of almost periodic system and Lyapunov function, we give some criteria which guarantee the existence and uniqueness and stability of almost periodic solutions of higher dimensional nonautono...By means of the properties of almost periodic system and Lyapunov function, we give some criteria which guarantee the existence and uniqueness and stability of almost periodic solutions of higher dimensional nonautonomous system. The result is more convenient and effective than the related result in[1].展开更多
王联等(“常差分方程,”220～222在‖f(k,y(k))‖≤g(k)‖y(k)‖,g(k)是正的,且sum from k=(?) to ∞(k)<∞;或‖f(k,y(k))‖≤L‖y(k)‖,L>0充分小的条件下得到了扰动线性差分方程(3)解的稳定性的几个定理。本文在未被扰动线性...王联等(“常差分方程,”220～222在‖f(k,y(k))‖≤g(k)‖y(k)‖,g(k)是正的,且sum from k=(?) to ∞(k)<∞;或‖f(k,y(k))‖≤L‖y(k)‖,L>0充分小的条件下得到了扰动线性差分方程(3)解的稳定性的几个定理。本文在未被扰动线性差分方程(2)有界增长的条件下,利用离散积分不等式经较定理,对上述问题得到了一些新的结果。展开更多
Here several theorems are established to discuss uniform stability and uniformasymptotical stability of zero solution for difference equations with time delay. Thesetheorems extend Razumikhin Method from functional di...Here several theorems are established to discuss uniform stability and uniformasymptotical stability of zero solution for difference equations with time delay. Thesetheorems extend Razumikhin Method from functional differential equations to time delaydifference equations.展开更多
In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case ...In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.展开更多
We consider Lienard system and obtain following conclusions: The zero solution of system x' + f(x)x' + g(x) = 0 is uniformly asymptotically stable if g(0) = 0, and (x) > 0. And system X' + f(x)x' ...We consider Lienard system and obtain following conclusions: The zero solution of system x' + f(x)x' + g(x) = 0 is uniformly asymptotically stable if g(0) = 0, and (x) > 0. And system X' + f(x)x' + g(x) = e(t) has uniformly asymptotically stable solutions if g(0) = 0, and Hence it has a unique almost odic solution when e(t) is almost periodic and it has a unique periodic solution when e(t) is periodic. In [1] Fink obtained above the second conclusion if sup In [2] we obtained same result if g(x) = cx.展开更多
文摘By means of the properties of almost periodic system and Lyapunov function, we give some criteria which guarantee the existence and uniqueness and stability of almost periodic solutions of higher dimensional nonautonomous system. The result is more convenient and effective than the related result in[1].
文摘王联等(“常差分方程,”220～222在‖f(k,y(k))‖≤g(k)‖y(k)‖,g(k)是正的,且sum from k=(?) to ∞(k)<∞;或‖f(k,y(k))‖≤L‖y(k)‖,L>0充分小的条件下得到了扰动线性差分方程(3)解的稳定性的几个定理。本文在未被扰动线性差分方程(2)有界增长的条件下,利用离散积分不等式经较定理,对上述问题得到了一些新的结果。
文摘Here several theorems are established to discuss uniform stability and uniformasymptotical stability of zero solution for difference equations with time delay. Thesetheorems extend Razumikhin Method from functional differential equations to time delaydifference equations.
文摘In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.
文摘We consider Lienard system and obtain following conclusions: The zero solution of system x' + f(x)x' + g(x) = 0 is uniformly asymptotically stable if g(0) = 0, and (x) > 0. And system X' + f(x)x' + g(x) = e(t) has uniformly asymptotically stable solutions if g(0) = 0, and Hence it has a unique almost odic solution when e(t) is almost periodic and it has a unique periodic solution when e(t) is periodic. In [1] Fink obtained above the second conclusion if sup In [2] we obtained same result if g(x) = cx.
