Homoclinic Solutions for a Class of Perturbed Fractional Hamiltonian Systems with Subquadratic Conditions.

In this paper, we consider the following perturbed fractional Hamiltonian systems { t D ∞ α (− ∞ D t α u (t)) + L (t) u (t) = ∇ u W (t , u (t)) + ∇ u G (t , u (t)) , t ∈ ℝ , u ∈ H α (ℝ , ℝ N) , where α ∈ (1 / 2 , 1 ] , L ∈ C (ℝ , ℝ N × N) is symmetric and not necessarily required to be positive definite, W ∈ C 1 (ℝ × ℝ N , ℝ) is locally subquadratic and locally even near the origin, and perturbed term G ∈ C 1 (ℝ × ℝ N , ℝ) maybe has no parity in u. Utilizing the perturbed method improved by the authors, a sequence of nontrivial homoclinic solutions is obtained, which generalizes previous results. [ABSTRACT FROM AUTHOR]