The authors consider the second order Hamiltonian system
where is a symmetric matrix valued function and . They use the variant fountain theorem to prove that the system (HS) possesses infinitely many homoclinic orbits, assuming that satisfies the coercive condition and satisfies the conditions that
() are even in ;
() There exist such that
() There exist and such that for all , moreover, uniformly for ;
() and uniformly for all
Conditions ()–() imply that is sub-quadratic and is super-quadratic, which generalize the sub-quadratic condition that
() where .
Reviewer’s remark: In the proof of Lemma 3.3, the authors say that “Set , then , and ”. It seems that this conclusion is incorrect.