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Infinitely many homoclinic orbits for the second-order Hamiltonian systems with super-quadratic potentials. (English) Zbl 1162.34328
Summary: We study the existence of infinitely many homoclinic orbits for some second-order Hamiltonian systems: $\ddot u - L(t)u(t)+\nabla F(t,u(t)) = 0, \forall t \in \bbfR$, by the variant fountain theorem, where $F(t,u)$ satisfies the super-quadratic condition $F(t,u)/|u|^{2}\rightarrow \infty $ as $|u|\rightarrow \infty $ uniformly in $t$, and need not satisfy the global Ambrosetti-Rabinowitz condition.

34C37Homoclinic and heteroclinic solutions of ODE
Full Text: DOI
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