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, PDF, 下载: 74  浏览: 119 
作者: 顾啸风：浙江师范大学，数学科学学院，浙江 金华
关键词: 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
摘要: 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 Ω 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。
Abstract: In this paper, we investigate the following critical elliptic equation with Stein-Weiss type convolution parts , (1) where α ≥ 0, N > 4, 0 < µ < N, 0 < 2α + µ < 4, and Ω 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.
文章引用：顾啸风. 具有 Stein-Weiss 卷积部分的临界椭圆型方程 的正解[J]. 应用数学进展, 2024, 13(5): 2110-2124. https://doi.org/10.12677/AAM.2024.135199

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