Existence of solutions to fractional Hamiltonian systems with local superquadratic conditions
Texas State University, Department of Mathematics
In this article, we study the existence of solutions for the fractional Hamiltonian system tDα∞ (-∞Dαtu(t)) + L(t)u(t) = ∇W(t, u(t)), u ∈ Hα (ℝ, ℝN), where tDα∞ and -∞Dαt are the Liouville-Weyl fractional derivatives of order 1/2 < α < 1, L ∈ C (ℝ, ℝNxN) is a symmetric matrix-valued function, which is unnecessarily required to be coercive, and W ∈ C1 (ℝ x ℝN, ℝ) satisfies some kind of local superquadratic conditions, which is rather weaker than the usual Ambrosetti-Rabinowitz condition.
Fractional Hamiltonian system, Variational method, Superquadratic
Guo, Z., & Zhang, Q. (2020). Existence of solutions to fractional Hamiltonian systems with local superquadratic conditions. <i>Electronic Journal of Differential Equations, 2020</i>(29), pp. 1-12.