Existence of homoclinic solutions for the non-autonomous fractional
Hamiltonian systems
Abstract
In this reseach work, we give a new result to guarantee the existence of
homoclinic solutions for the nonperiodic fractional Hamiltonian systems
-_{t}D_{∞}^{α}(_{-∞}D_{t}^{α}x(t))-L(t)x(t)+∇W(t,x(t))=0,
where α∈(1/2,1], x∈H^{α}(R,R^{N}), W∈C¹(R×R^{N},R). We
assume that W(t,x) do not satisfy the global Ambrosetti-Rabinowitz
condition and is not necessary periodic in t. This result generalizes
and improves some existing results in the literature.