一类二阶非Hamiltonian系统的变分原理及周期解的存在性定理

Variational principle and existence theorems of periodic solutions for a class of second order non-Hamiltonian systems

研究了阻尼振动问题{(t)+g(t)(t)=▽F(t,u(t)),a.e.t∈[0,T];u(0)-u(T)=(0)-(T)=0.其中,T>0,g(t)∈L∞(0,T;R),G(t)=integral from n=0 to t g(s)ds,G(T)=0,F:[0,T]×RN→R.给出了其变分原理和2个周期解的存在性定理.即使在g(t)=0特殊情况下,所得结果也是新的.

The following damped vibration problem was studied,{ü（t）＋g（t）u（t）=△F（t,u（t））,a.e.t∈[0,T]; u（0）-u（T）=u（0）-u（T）=0where T〉0,g（t）∈L^∞（0,T,R）,G（t）=∫^tog（s）ds,G（T）=0,F;[0,T]×R^N→R.The variational principle and two existence theorems for periodic solutions were given. In the special case while g（t） = 0 the results presented was also a new result.