In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equa...In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a（t）, b（t） and e（t） are periodic functions, and this solution is an almost periodic solution if a（t）, b（t） and e（t） are almost periodic functions.展开更多
The main goal of this paper is to compute the Figure-eight solutions for the planar Newtonian 3-body problem with equal masses by finding the critical points of the functional associated with the motion equations of 3...The main goal of this paper is to compute the Figure-eight solutions for the planar Newtonian 3-body problem with equal masses by finding the critical points of the functional associated with the motion equations of 3-body in plane R2. The algorithm adopted here is the steepest descent method, which is simple but very valid for our problem.展开更多
In this paper, we improve LaSalle＇s invariance theorem based on Li＇s work （Li Yong, Asymptotic stability and ultimate boundedness, Northeast. Math. J., 6（1）（1990）, 53-59） by relaxing the restrictions, which ma...In this paper, we improve LaSalle＇s invariance theorem based on Li＇s work （Li Yong, Asymptotic stability and ultimate boundedness, Northeast. Math. J., 6（1）（1990）, 53-59） by relaxing the restrictions, which make the theorem more easy to apply. In addition, we also improve LaSalle＇s theorem for stochastic differential equation established by Mao （Mao Xuerong, Stochastic versions of the LaSalle theorem, J. Differential Equations, 153（1999）, 175-195）.展开更多
文摘In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a（t）, b（t） and e（t） are periodic functions, and this solution is an almost periodic solution if a（t）, b（t） and e（t） are almost periodic functions.
文摘The main goal of this paper is to compute the Figure-eight solutions for the planar Newtonian 3-body problem with equal masses by finding the critical points of the functional associated with the motion equations of 3-body in plane R2. The algorithm adopted here is the steepest descent method, which is simple but very valid for our problem.
基金The 985 Project of Jilin University and Graduate Innovation Lab of Jilin University.
文摘In this paper, we improve LaSalle＇s invariance theorem based on Li＇s work （Li Yong, Asymptotic stability and ultimate boundedness, Northeast. Math. J., 6（1）（1990）, 53-59） by relaxing the restrictions, which make the theorem more easy to apply. In addition, we also improve LaSalle＇s theorem for stochastic differential equation established by Mao （Mao Xuerong, Stochastic versions of the LaSalle theorem, J. Differential Equations, 153（1999）, 175-195）.
