具有 Stein-Weiss 卷积部分的临界椭圆型方程 的正解

Positive Solution for the Critical Elliptic Equation with Stein-Weiss Type Convolution Parts

本文研究了具有 Stein-Weiss 卷积部分的临界椭圆方程, (1) 其中 α ≥ 0,N > 4,0 且 Ω 是 RN 中包含原点的C1 开有界域。我们证明了当 > 0 且 2 α,µ时,方程 (2) 存在一个正的基态解。

In this paper, we investigate the following critical elliptic equation with Stein-Weiss type convolution parts , (1) where α ≥ 0, N > 4, 0 and Ω is a C1 open bounded domain in RN that contains the origin. We show that when > 0 and 2 α,µ , problem (2) possesses a positive ground state solution.