We investigate a class of Hamiltonian systems \(\begin{array}{l}-{q}^{^{\prime\prime} }\left(t\right)+\left(L\left(t\right)-\xi \right)q\left(t\right)=a\left(t\right){\left|q\left(t\right)\right|}^{p-2}q\left(t\right)+nf\left(t\right),\\ q\in {H}^{1}\left({\mathbb{R}},{\mathbb{R}}^{N}\right),\end{array}\)
where (t, q) ∈ ℝ × ℝN, p > 2, a ∈ C(ℝ, (0,+∞)), f ∈ C(ℝ, ℝN), ξ, η are real parameters, and L ∈ C(ℝ, \({\mathbb{R}}^{{N}^{2}}\) ) is a positive-definite symmetric matrix for all t ∈ ℝ. Our main technical approach is based on the Nehari-manifold method combined with variational and topological methods. The obtained results extend and complement the results available in the literature.
