MULTIPLE SOLUTIONS FOR A CLASS OF FRACTIONAL HAMILTONIAN SYSTEMS

作者：Xu Jiafa^*; O'Regan Donal; Zhang Keyu

来源：Fractional Calculus and Applied Analysis, 2015, 18(1): 48-63.

DOI：10.1515/fca-2015-0005

• fractional Hamiltonian system
• critical point
• variational methods
• multiple solutions

In this paper, we establish two existence theorems for multiple solutions for the following fractional Hamiltonian system
{tD(infinity)(alpha)((-infinity)D(t)(alpha)u(t)) + L(t)u(t) = del W(t, u(t)),
u is an element of H-alpha(R, R-N),
where (alpha) is an element of (1/2, 1), t is an element of R, u = (u(1),..., u(N)) T is an element of R-N, and L is an element of C(R, R-N2) is a symmetric and positive definite matrix for all t is an element of R, W is an element of C-1(R x R-N, R), and del W is the gradient of W about u.

• 出版日期2015-2
• 单位山东大学; 齐鲁师范学院