不满足Gordon-强力条件的奇异二阶周期Hamilton系统同宿轨道的存在性

NONTRIVIAL HOMOCLINIC ORBITS FOR SINGULAR SECOND ORDER PERIODIC HAMILTONIAN SYSTEMS NOT SATISFYING GORDON-STRONG FORCE CONDITION

考虑奇异的二阶周期 Hamilton 系统这里q=(q_1,q_2,…,q_n)∈R^n,n>2,V(t,q):R×R^n\{e}→R 是一个奇异的位势函数,e≠0.当V(t,q)具有唯一最大值,但不满足 Gordon- 强力条件时,我们证明了(HS)至少具有一条非平凡的同宿轨道。

The ekistence of nontrivial homoclinic orbits of periodic Hamiltonian systems: q+V′_q(t,q) =0 (HS) is proved, where q=(q1, q2,…,q_n), n>2, V(t, q): R^1×R^n\{e}→R^1 is a potential with a singularity i.e. -V(t,q)→∞,as q→e.Our main assumptions are lack of Gordon-Strong Force condion and the uniqueness of a global maximu of V(t, q).