R3中 p-curl-div 系统解的存在性
Existence of Nontrivial Solutions for p-curl-div System in R 3
DOI:10.12677/AAM.2024.134177,PDF,下载: 159浏览: 255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 ∈ R 3非平凡解的存在性，其中，1 < p < 3, f (x, u) : R 3× R 3→ R 3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 ∈ R 3and establish the existence of solution, where 1 < p < 3, f (x, u) : R 3× R 3→ R 3satisfies some reasonable hypothesis.
文章引用：杨洋, 滕凯民. R 3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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