二阶Hamilton系统具相关性质的次调和解的存在性

Subharmonic solutions with certain properties for second order Hamiltonian system

给出了二阶非自治Hamilton系统ü(t)+▽F(t,u(t))=0,a.e.t∈R在势函数是次线性的情况下具有相关性质且极小化泛函的次调和解的存在条件,得到了在某个方向上存在无穷多个具有这些性质的次调和解的存在准则,推广了文献中的一些结果.

The existence of subharmonic solutions with some extra properties for the following non-autonomous second order Hamiltonian system u（t）＋ F（t,u（t））=0,a.e.t∈R was studied under the condition that the potential function was sub-linear. Some new criterions were obtained for guaranteeing that the problem had infinitely distinct subharmonic solutions in some direction. Recent results from the literature were significantly improved.