二阶非自治Hamilton系统多周期解的存在性

Existence of multiple periodic solutions for non-automous second order Hamiltonian systems

研究如下一类非自治二阶Hamilton系统ü(t)=F(t,u(t))+e(t),a.e.t∈[0,T],u(0)-u(T)=u.(0)-u.(T)=0。将非线性项分为自治或非自治两部分,在满足部分周期,线性,次线性及其他一些限制条件,应用临界点理论中的极小极大原理,证明周期解的多重存在性,获得了一些有意义的结果。

The following non-autonomous second order Hamiltonian system{üD（t）=F（t,u（t））＋e（t）,a.e.t∈,u（0）-u（T）=u·（0）-u·（T）=0.is considered.The nonlinearity is assumed to divide into automous and non-automous parts and satisfies some periodicity,linearity,sub-linearity and other conditions.Under these assumptions,some meaningful results on the existence and multiplicity of periodic solutions are obtained by using minimax priciple in critical point theory.