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[1]吴燕林,钱晓涛.全空间上一类Kirchhoff型问题正基态解的存在性[J].延边大学学报(自然科学版),2021,47(01):17-20.
　WU Yanlin,QIAN Xiaotao.Existence of ground state positive solution for a class of Kirchhoff type problem on unbounded domain[J].Journal of Yanbian University,2021,47(01):17-20.

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全空间上一类Kirchhoff型问题正基态解的存在性

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第47卷期数: 2021年01期页码: 17-20 栏目: 基础科学研究出版日期: 2021-04-20

Title:: Existence of ground state positive solution for a class of Kirchhoff type problem on unbounded domain

文章编号:: 1004-4353(2021)01-0017-04

作者:: 吴燕林; 钱晓涛; ( 阳光学院基础教研部, 福建福州 350015 )

Author(s):: WU Yanlin; QIAN Xiaotao; (Department of Basic Teaching and Research, Yango University, Fuzhou 350015, China)

关键词:: Kirchhoff问题; 正基态解; 变分方法; Nehari流形; 集中紧性原理

Keywords:: Kirchhoff problem; ground state positive solution; variational method; Nehari manifold; concentration compact principle

分类号:: O175.2

文献标志码:: A

摘要:: 在全空间上应用Nehari流形和集中紧性原理研究了如下一类Kirchhoff型问题:{ -(a+b∫_{R^_</sup>N}|䥺SymbolQC@u|²dx)Δu+u=Q(x)|u|^{p -2}u, x∈R^N; u∈H¹(R^N), u>0, x∈R^N,并证明了该问题至少存在一个正基态解.该结果补充了文献[1-4]关于正基态解的存在性结果.

Abstract:: We study the following class of Kirchhoff type problem on unbounded domain { -(a+b∫_{R^_</sup>N}|䥺SymbolQC@u|²dx)Δu+u=Q(x)|u|^{p -2}u, x∈R^N; u∈H¹(R^N), u>0, x∈R^N, and prove the existence of at least one ground state positive solution by using Nehari manifold and concentration compact principle. The result can be seen as a supplement of literature [1-4] concerning the existence of ground state positive solution.

参考文献/References:

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[2] BAHRI A, LIONS P L. On the existence of a positive solution of semilinear Elliptic equations in unbounded domains[J]. Annales De L Institut Henri Poincare -Analysis Non Linear, 1997,14(3):365-413.
[3] HE X M, ZOU W M. Existence and concentration behavior of positive solutions for a Kirchhoff equation in R³[J]. Journal of Differential Equations, 2012,252(2):1813-1834.
[4] WANG J, TIAN L X, XU J X, et al. Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth[J]. Journal of Differential Equations, 2012,253(7):2314-2351.
[5] CHEN J Q. Multiple positive solutions to a class of Kirchhoff equation on R³ with indefinite nonlinearity[J]. Nonlinear Analysis, 2014,96:134-145.
[6] QIAN X T, CHAO W. Existence of positive solutions for nonlocal problems with indefinite nonlinearity[J]. Boundary Value Problems, 2020,40:1-13.
[7] LIONS P L. The concentration -compactness principle in the calculus of variations[J]. Annales De Linstitut Henri Poincare Non Linear Analysis, 1984,1:223-283.
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备注/Memo

收稿日期: 2020-11-25
基金项目: 福建省教育厅中青年教师教育科研项目(JAT170772)
作者简介: 吴燕林(1984—),女,副教授,研究方向为非线性分析及其应用.

更新日期/Last Update: 2021-04-20