带临界指数的分数阶Schrödinger方程解的存在性

Existence of fractional Schrödinger equation solutions with critical exponents

研究一类带临界指数的分数阶Schrödinger方程解的存在性。在扰动项满足较弱的条件下,利用山路定理证明了方程至少具有一个非平凡解。

In this paper,we study the existence of solutions to a class of fractional Schrödinger equations with critical exponents.For some weak conditions on the perturbation term,it is proved by the mountain pass theorem that the equation has at least one non-trivial solution.