一类带有不定位势Kirchhoff方程多重解的存在性

兰州理工大学学报 ›› 2024, Vol. 50 ›› Issue (4): 168-172.

• 数理科学 • 上一篇

一类带有不定位势Kirchhoff方程多重解的存在性

陈林松, 胡天群, 周鉴^*

贵州师范大学数学科学学院, 贵州贵阳 550000

收稿日期:2023-01-07 出版日期:2024-08-28 发布日期:2024-08-30
通讯作者: 周鉴(1976-),男,上海人,副教授.Email:zhoujiandepict@163.com
基金资助:
贵州省基础研究计划(自然科学项目)(黔科合基础-ZK[2022]一般318)

The existence of multiple solutions for a Kirchhoff-type equation with indefinite

CHEN Lin-song, HU Tian-qun, ZHOU Jian

School of Mathematical Sciences, Guizhou Normal University, Guiyang 550000, China

Received:2023-01-07 Online:2024-08-28 Published:2024-08-30

摘要/Abstract

摘要： 研究R^N中一类带有不定位势的Kirchhoff方程,其中位势函数是可变号的.利用Morse理论和变分学原理,得到方程多重解的存在性.

关键词: Kirchhoff方程, 不定位势, (PS)条件, Morse理论, 变分学原理

Abstract: A Kirchhoff-type equation in R^N with the indefinite potential is studied here. The existence of multiple solutions is obtained for the equation via Morse theory and variational methods.

Key words: Kirchhoff equation, indefinite potential, (PS)condition, Morse theory, variational theory

中图分类号:

O177.91

陈林松, 胡天群, 周鉴. 一类带有不定位势Kirchhoff方程多重解的存在性[J]. 兰州理工大学学报, 2024, 50(4): 168-172.

CHEN Lin-song, HU Tian-qun, ZHOU Jian. The existence of multiple solutions for a Kirchhoff-type equation with indefinite[J]. Journal of Lanzhou University of Technology, 2024, 50(4): 168-172.

参考文献

[1] KIRCHHOFF G.Mechanik [M].Teubner:Leipzig,1883.
[2] LIONS J L.On some questions in boundary value problems of mathematical physics [J].Science Direct,1978,30:284-346.
[3] AROSIO A, PANIZZI S.On the well-posedness of the Kirchhoff string [J].Trans Amer Math Soc,1996,348(1):305-330.
[4] MAO A, ZHANG Z.Sign-changing and multiple solutions of Kirchhoff type problems without the P.S.condition [J].Nonlinear Analysis,2009,70:1275-1287.
[5] ZHANG J,TANG X H,ZHANG W.Infinitely many solutions of quasilinear Schrödinger equation with sign-changing potential [J].Journal of Mathematical Analysis and Applications,2014,420:1762-1775.
[6] XU L, CHEN H.Nontrivial solutions for Kirchhoff-type problems with a parameter [J].Journal of Mathematical Analysis and Applications,2016,433:455-472.
[7] PERERA K,ZHANG Z.Nontrivial solutions of Kirchhoff-type problems via the Yang index [J].Journal of Differential Equations,2006,221:246-255.
[8] CHEN S,LIU S.Standing waves for 4-superlinear Schrödinger-Kirchhoff equations [J].Mathematical Methods in the Applied Sciences.2014,38:2185-2193.
[9] LIU W,HE X.Multiplicity of high energy solutions for superlinear Kirchhoff equations [J].Journal of Applied Mathematics and Computing,2012,39:473-487.
[10] WU X.Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations inR³ [J].Nonlinear Analysis:Real World Applications,2011,12:1278-1287.
[11] HE X M,ZOU W M.Infinitely many positive solutions for Kirchhoff-type problems [J].Nonlinear Analysis,2009,70:1407-1414.
[12] BARTSCH T,WANG Z Q.Existence and multiplicity results for some superlinear elliptic problems on R^N[J].Communications in Partial Differential Equations,1995,20:1725-1741.
[13] REED M,SIMON B.Methods of modern mathematical physics [M].Academic Press:Analysis of Operators,1978.
[14] CHANG K C.Infinite dimensional morse theory and multiple solution problems [M].Boston:Birkhäuser,2012.
[15] LIU Z,WANG Z Q.On Clark’s theorem and its applications to partially sublinear problems [J].Annales De Linstitut Henri Poinc are Analye Non Lineaire,2015,32:1015-1037.

一类带有不定位势Kirchhoff方程多重解的存在性

The existence of multiple solutions for a Kirchhoff-type equation with indefinite

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价