Multiple positive solutions for a logarithmic Kirchhoff type problem in R3

被引：9

作者：

Gao, Yuan ^{[1
,2
]}

Jiang, Yongsheng ^{[3
]}

Liu, Lishan ^{[2
]}

Wei, Na ^{[3
]}

机构：

[1] Qufu Normal Univ, Sch Stat & Data Sci, Qufu 273165, Shandong, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[3] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Hubei, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2023年 / 139卷

关键词：

Kirchhoff type problem; Logarithmic nonlinearity; Positive solutions; EXISTENCE; EQUATIONS;

D O I：

10.1016/j.aml.2022.108539

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By using the variational methods and the maximum principle, we investigate the following logarithmic Kirchhoff type problem ( integral ) a+b| backward difference u|2 +V(x)u2dx [- increment u +V(x)u] = |u|p-1ulog|u|, (P) R3 where a > 0, b > 0, 1 < p < 3. Under some assumptions on the potential function V(x), we prove that (P) has only trivial solution for large b > 0; and (P) owns two positive solutions for small b > 0. Moreover, we obtain that the value of parameter b determines the number of positive solutions under the effects of both local term and nonlocal term. (c) 2022 Elsevier Ltd. All rights reserved.

引用

页数：6

共 21 条

[1] Existence of a positive solution for a logarithmic Schrodinger equation with saddle-like potential [J].

Alves, Claudianor O. ;

Ji, Chao .

MANUSCRIPTA MATHEMATICA, 2021, 164 (3-4) :555-575

[2] Positive solutions for a quasilinear elliptic equation of Kirchhoff type [J].

Alves, CO ;

Corrêa, FJSA ;

Ma, TF .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (01) :85-93

[3]

[Anonymous], 1978, N HOLLAND MATH STUDI, DOI DOI 10.1016/S0304-0208(08)70870-3

[4]

[Anonymous], 1997, Minimax Theorems

[5] EXISTENCE AND MULTIPLICITY RESULTS FOR SOME SUPERLINEAR ELLIPTIC PROBLEMS ON R(N) [J].

BARTSCH, T ;

WANG, ZQ .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1995, 20 (9-10) :1725-1741

[6] Existence results of positive solutions of Kirchhoff type problems [J].

Cheng, Bitao ;

Wu, Xian .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (10) :4883-4892

[7] Existence and concentration behavior of positive solutions for a Kirchhoff equation in R3 [J].

He, Xiaoming ;

Zou, Wenming .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (02) :1813-1834

[8]

He Y, 2014, ADV NONLINEAR STUD, V14, P483

[9]

[胡蝶 Hu Die], 2022, [数学物理学报. A辑, Acta Mathematica Scientia], V42, P401

[10] MULTIPLICITY OF POSITIVE SOLUTIONS FOR KIRCHHOFF TYPE PROBLEMS IN R3 [J].

Hu, Tingxi ;

Lu, Lu .

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2017, 50 (01) :231-252

← 1 2 3 →