一类阻尼振动问题的变分原理及周期解的存在性定理(英文)

Variational Principle and Existence Theorems of Periodic Solutions for a Class of Damped Vibration Problems

对如下的阻尼振动问题:{ (t)+g(t)(t)=F(t,u(t)),a.e.t∈[0,T],u(0)-u(T)=(0)-(T)=0.此处,T >0,g∈ L^1(0,T,;R),G(t)=01∫g(s)ds,G(T) =0,F:[0,T]×R^N→ R,给出其变分原理,并得到2个周期解的存在性定理.

In the present paper, we research the following damped vibration problem {ü（t）＋g（t）^·u（t）=△↓F（t,u（t））,a.e.t∈[0,T], u（0）-u（T）=^·u（0）-·u（T）=0. where T〉0,g∈L^1（0,T,;R）,G（t）=∫0^1g（s）ds,G（T）=0 and F：[0,T]×R^H→R. The variational princi- ple is given, and two existence theorems of periodic solutions are obtained.