(untitled) (Communications in Mathematical Research, 2025)
This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forcing perturbations q+Aq+V_q(t,q)= f(t), where q= (q_1,q_2,···,q_N)∈R^N, A is an antisymmetric constant N×N matrix, V(t,q) = −K(t,q)+W(t,q) with K,W ∈ C^1 (R,R^N) and satisfying b_1|q|^2 ≤ K(t,q) ≤ b_2|q|^2 for some positive constants b_2 ≥b_1 >0 and external forcing term f ∈C(R,R^N) being small enough. Under some new weak superquadratic conditions for W, by using the mountain pass theorem, we obtain the existence of at least one nontrivial homoclinic solution.