关键词: 多重解, 周期解, 分数阶Laplace算子, Clark定理

Abstract: By using variational method, critical point theory and truncation techniques, we studied the multiplicity of periodic solutions for a class of nonlinear fractional Laplacian system. When the nonlinear term satisfies appropriate conditions, we prove that for any positive integer k>0, the system has k pairs of periodic solutions with period T.

Key words: multiple solution, periodic solution, fractional Laplacian operator, Clark’s theorem