高次分数阶Laplace方程的Liouville定理

A Liouville Theorem for the Higher Order Fractional Laplacian

考虑上半空间中非局部高次分数阶微分方程解的不存在性,建立无界区域上高次分数阶方程的无穷退化原理。在此基础上,利用迭代法,证明一类具有Navier条件的高次分数阶方程正解的不存在性。

We consider the nonexistence of Solutions of Non-local Higher Order Fractional Differential Equations in the First Half Space. First, a decay at infinity for higher order fractional equations in a unbounded domain is established and then nonexistence of positive solutions for higher order fractional elliptic equations with the complementary Navier conditions is proved by using iterative method.