更高分数阶Laplacian方程的径向解

Radial Solutions of Fractional Laplacian Equations

主要研究了一类分数阶Laplacian方程的径向解问题。在分数阶径向Sobolev空间Wrs,2(RN)中,通过相关定理获得所取极小化序列的估计,对方程的泛函利用变分法、约束极值获得了解的对称性结果。获得的结果与经典的p-Laplacian方程以及Schrӧdinger方程一致。

This paper mainly studies the radial solution of a class of fractional Laplacian equations. In the fractional radial Sobolev space Wrs,2(RN), the estimation of the minimization sequence is obtained by using the correlation theorem, and the symmetry results of the solution are obtained by using the variational method and constrained extremum for the functional of the equation. The results obtained are consistent with the classical p-Laplacian equation and Schrodinger equation.