R3 中 p-curl-div 系统解的存在性

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R³ 中 p-curl-div 系统解的存在性
Existence of Nontrivial Solutions for p-curl-div System in R³

DOI: 10.12677/AAM.2024.134177, PDF, 下载: 130 浏览: 209 科研立项经费支持
作者: 杨洋, 滕凯民：太原理工大学数学学院，山西晋中
关键词: p-curl-div系统；变分发；弱解；p-curl-div System； Variational Approach； Weak Solution

摘要: 本文采用变分法研究如下的 p-curl-div 方程 ∇ × (|∇ × u|^p−2∇ × u) − ∇(|divu|^p−2divu) = f (x, u), x ∈ R³ 非平凡解的存在性，其中，1 < p < 3, f (x, u) : R³ × R³ → R³ 满足一些合理性假设。

Abstract: In this paper, we study the following p-curl-div system ∇ × (|∇ × u|^p−2∇ × u) − ∇(|divu|^p−2divu) = f (x, u), x ∈ R³ and establish the existence of solution, where 1 < p < 3, f (x, u) : R³ × R³ → R³ satisfies some reasonable hypothesis.

文章引用：杨洋, 滕凯民. R³ 中 p-curl-div 系统解的存在性[J]. 应用数学进展, 2024, 13(4): 1882-1904. https://doi.org/10.12677/AAM.2024.134177

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