Homoclinic Solutions for Second-order Non-autonomous Hamiltonian Systems without Global Ambrosetti-rabinowitz Conditions
نویسندگان
چکیده
This article studies the existence of homoclinic solutions for the second-order non-autonomous Hamiltonian system q̈ − L(t)q + Wq(t, q) = 0, where L ∈ C(R, Rn ) is a symmetric and positive definite matrix for all t ∈ R. The function W ∈ C1(R × Rn, R) is not assumed to satisfy the global Ambrosetti-Rabinowitz condition. Assuming reasonable conditions on L and W , we prove the existence of at least one nontrivial homoclinic solution, and for W (t, q) even in q, we prove the existence of infinitely many homoclinic solutions.
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