兰州大学机构库 >数学与统计学院
带磁场的非线性Schrödinger方程解的存在性
Alternative TitleExistence of solution of nonlinear Schrödinger equation with magnetic field
胡杭洲
Thesis Advisor赵敦
2018-03-30
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
KeywordSchrödinger方程 磁场 解的存在性 集中紧性
Abstract

本文研究带磁场的 Schrödinger 方程解的存在性. 在 A 和 V 满足适当条件时, 利用 Nehari 流形技巧, 我们给出了如下方程
−ΔAu + V (x)u = |u|p−2u + λ|u|r−2u, u(x) ∈ H1A(RN)基态解的存在性, 其中 2 < r < p < 2*, λ ∈ R. 进一步, 我们给出了带磁场的Sobolev 空间上集中紧性原理的一种抽象形式, 并利用这一框架给出了一类带磁场 Schrödinger 方程解的存在性.

Other Abstract

In this paper we consider the existence of solution for nonlinear Schrödinger equation with an external magnetic field. Firstly, under appropriate assumptions on A and V , applying Nehari manifold technique, we prove the existence of ground state solution for the following equation
−ΔAu + V (x)u = |u|p−2u + λ|u|r−2u, u(x) ∈ H1A(RN)

where 2 < r < p < 2*, λ ∈ R. Furthermore, we give an abstract form for the concentration-compacteness principle on the space H1A(RN), and give an example as an application.

URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225560
Collection数学与统计学院
Recommended Citation
GB/T 7714
胡杭洲. 带磁场的非线性Schrödinger方程解的存在性[D]. 兰州. 兰州大学,2018.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Altmetrics Score
Google Scholar
Similar articles in Google Scholar
[胡杭洲]'s Articles
Baidu academic
Similar articles in Baidu academic
[胡杭洲]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[胡杭洲]'s Articles
Terms of Use
No data!
Social Bookmark/Share
No comment.
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.