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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

DOI: 10.12677/AAM.2024.135199, PP. 2110-2124

Keywords: 临界椭圆方程,Stein-Weiss 卷积项,Nehari 流形,基态解
Critical Elliptic Equation
, Stein-Weiss Convolution Part, Nehari Manifold, Ground State Solution

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Abstract:

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 < μ < N,0 < 2α + μ < 4,\"\"且 ? 是 RN 中包含原点的C1 开有界域。我们证明了当 > 0 且 2 < p < 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 \"\", (2) where α ≥ 0, N > 4, 0 < μ < N, 0 < 2α + μ < 4, \"\"and ? is a C1 open bounded domain in RN that contains the origin. We show that when > 0 and 2 < p < 2?α,μ , problem (2) possesses a positive ground state solution.

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