A new method for the periodic solution of strongly nonlinear system is given. By using this method, the existance and stability of the periodic solution can be decided, and the approximate expression of the periodic s...A new method for the periodic solution of strongly nonlinear system is given. By using this method, the existance and stability of the periodic solution can be decided, and the approximate expression of the periodic solution can also be found.展开更多
I. Introduction In this paper we are looking for solutions of the following Hamiltonian system of second order: where x= （x1, x2） and V satisfies （V. 1） V: R×R2→R is a C1-function, 1-periodic In t, （V.2） V...I. Introduction In this paper we are looking for solutions of the following Hamiltonian system of second order: where x= （x1, x2） and V satisfies （V. 1） V: R×R2→R is a C1-function, 1-periodic In t, （V.2） V is periodic in x1 with the period T>0, （V. 3） V→O, Vx→O as |x2|→∞, uniformly in （t, x1）.展开更多
In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for stud...In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear systems. The periodic solution of Duffing equation is calculated by means of our method.展开更多
基金The project supported by the National Natural Science Foundation of China
文摘A new method for the periodic solution of strongly nonlinear system is given. By using this method, the existance and stability of the periodic solution can be decided, and the approximate expression of the periodic solution can also be found.
文摘I. Introduction In this paper we are looking for solutions of the following Hamiltonian system of second order: where x= （x1, x2） and V satisfies （V. 1） V: R×R2→R is a C1-function, 1-periodic In t, （V.2） V is periodic in x1 with the period T>0, （V. 3） V→O, Vx→O as |x2|→∞, uniformly in （t, x1）.
文摘In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear systems. The periodic solution of Duffing equation is calculated by means of our method.
