位势符号可变的非周期超二次Hamilton系统的同宿轨道

HOMOCLINIC ORBITS OF SUPERQUADRATIC HAMILTONIAN SYSTEMS NON-PERIODICITY WITH CHANGABLE POTENTIAL SIGN

研究了二阶Hamilton系统u··(t) -L(t)u(t) +V′u(t,u) =0 ,当位势函数V(t,u)可改变符号 ,非周期 ,且满足超二次条件 βV(t,u) -V′(t,u)≤α(L(t)u ,u) ) ,t∈R ,u∈Rm ,β>2 ,0≤α<β2 - 1时 ,用变分方法证明了该系统存在非平凡的同宿轨道 .

The existence of nontrivial homoclinic orbits of Hamiltonian systems u··(t)-L(t)u(t)+V′ u(t,u)=0, -∞<t<+∞ is proved, where V(t,u) is a non-periodic, superquadratic potential function with changable sign, namely βV(t,u)-V′(t,u)≤α(L(t)u,u)),t∈R,u∈R\+m,β>2,0≤α<β2-1. Via the variational method.