位势可变号的二阶奇异Hamilton系统的周期解

Periodic Solutions of Second Order Singular Hamiltonian Systems with Potentials Changing Sign

证明了位势可变号的二阶奇异Hamilton系统■+aq+W′(q)=0在W(q)满足Gordon-强力条件且有唯一最大值时,具有非平凡的T-周期解.

The existence of nontrivial T-periodic solutions of second order singular Hamiltonian systems q＋ aq ＋ W^1（q） =0 is proved, where a 〈 （π/T）^2 and W（q） 〈0, V qε R^n ／ {0,e}; W（0） =0; - W（ q ）→∞（q→e）. The main assumptions are Gordon -Strong Force condition and the uniqueness of a global maximum of W（ q ）.