SameexistenceandmultiplicityofhomoclinicorbitforsecondorderHamiltoniansystem¨↑x-a（t)x+Wx(t,x)=0aregivenbymeansofvariationalmethods,wherethepotentialV(t,x)=-1/2a（t)|s|^2+W(t,s)isquadraticinsatinfinityandsubquadraticinsatzero,andthefunctiona（t)satisfiesthegrowthconditionlimt→∞∫t…t+la（t)dt=+∞，A↓ι∈R^1.
