Subharmonic solutions for nonautonomous sublinear second order Hamiltonian systems

Some existence theorems are obtained for subharmonic solutions of nonautonomous second order Hamiltonian systems by the minimax methods in critical point theory.     

Periodic solutions for some nonautonomous second order Hamiltonian systems

The existence and multiplicity of periodic solutions are obtained for nonautonomous second order Hamiltonian systems by the minimax methods in critical point theory.     

Periodic solutions to differential systems with unbounded or periodic nonlinearities

We investigate the existence of (multiple) solutions of differential systems of Josephson-type with unbounded or periodic nonlinearities. Some new results are obtained and some results in the literature are improved.     

Periodic solutions for second order systems at resonance

The existence and multiplicity results are obtained for periodic solutions of second order systems at resonance with unbounded nonlinearity. The proofs rely on the minimax methods and an interesting integral inequality.     

Periodic solutions for a class of nonautonomous subquadratic second order Hamiltonian systems

Some existence theorems are obtained for periodic solutions of a class of unbounded nonautonomous nonconvex subquadratic second order Hamiltonian systems by using the minimax methods in critical point theory.     

非自治二阶Hamilton系统的周期解

本文推广了Willem的一个结果,Willem研究的受迫周期振动要求受迫势能关于空间变量是周期的,而本文只要求受迫势能对时间变量积分后关于空间变量是周期的,该结果包括了单摆的受迫振动.本文将用直接变分最小方法和Rabinowtz的鞍点定理来研究当势函数对时间变量积分后是周期时受迫摆方程的周期解.     

Periodic solutions for second order Hamiltonian systems with a change sign potential

An existence theorem is obtained for periodic solutions of nonautonomous second order Hamiltonian systems with a change sign potential by the minimax methods in critical point theory.     

Periodic solutions for nonautonomous second order systems with sublinear nonlinearity

The existence and multiplicity of periodic solutions are obtained for nonautonomous second order systems with sublinear nonlinearity by using the least action principle and the minimax methods.

     

Periodic solutions to second order nonautonomous differential systems with gyroscopic forces

Existence of periodic solutions to second order differential systems with gyroscopic forces is considered via variational methods, where a generalized Ahmad–Lazer–Paul type condition is used. We do not impose the condition that the gyroscopic forces are small.     

Periodic solutions of a second order forced sublinear differential equation with delay

In this paper, existence criteria are established for the existence of periodic solutions of a second order sublinear differential equation with delay and forcing function. Our method is based on careful a priori estimation and continuation theorems, and our sublinear condition is an improvement of the boundedness condition in some recent results.