Homoclinic solutions for a class of non-autonomous subquadratic second-order Hamiltonian systems

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Existence and uniqueness of solutions for a fractional boundary value problem on a graph (2014, background): “For more studies on homoclinic solutions for difference equations, we refer the reader to [1, 3, 4, 6, 7, 9, 11] and the references therein.”
Homoclinic solutions for a class of subquadratic second-order Hamiltonian systems (2011, background): “1 of [17], we obtain that the critical points of φ are classical solutions of (HS) satisfying u ∈ C2(R,RN ), u(t) → 0 and u̇(t) → 0 as |t| → ∞.”