Infinitely many small energy solutions for Fourth-Order Elliptic Equations with p-Laplacian in RN

被引：2

作者：

Chahma, Youssouf ^{[1
,2
]}

Chen, Haibo ^{[1
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Univ Sci & Technol Houari Boumed, Fac Math, PB 32, Algiers 16111, Algeria

来源：

APPLIED MATHEMATICS LETTERS | 2023年 / 144卷

关键词：

Variational methods; Fourth-order elliptic equations; p-Laplacian; Infinitely many small energy;

D O I：

10.1016/j.aml.2023.108728

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following fourth-order elliptic equation with p-Laplacian, steep potential well and sublinear perturbation: A2u -Apu & mu;V (x)u = f(x, u) & xi;(x)IuIq-2u, x E RN , where N > 5, A2 := A(A) is the biharmonic operator, Apu = div (IvuIp-2vu) with p > 2, & mu; > 0 is a parameter, f E C (RN x R , R) , & xi; E L2-4 (RN) with 2 1 < q < 2, we have the potential V E C(RN , R), and V-1(0) has nonempty interior. Under certain assumptions on V and f , we show the existence nontrivial solutions by virtue of variational methods, the existence criteria of infinitely many nontrivial small energy solutions are established.& COPY; 2023 Elsevier Ltd. All rights reserved.

引用

页数：8

共 50 条

[1] Infinitely many solutions for a class of quasilinear elliptic equations with p-Laplacian in RN
Gao Jia
Jie Chen
Long-jie Zhang
[J]. Boundary Value Problems, 2013
[2] Infinitely many solutions for a class of quasilinear elliptic equations with p-Laplacian in RN
Jia, Gao
Chen, Jie
Zhang, Long-jie
[J]. BOUNDARY VALUE PROBLEMS, 2013,
[3] Infinitely many solutions for fourth-order elliptic equations
Ye, Yiwei
Tang, Chun-Lei
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 394 (02) : 841 - 854
[4] INFINITELY MANY SOLUTIONS FOR A CLASS OF MODIFIED NONLINEAR FOURTH-ORDER ELLIPTIC EQUATIONS ON RN
Che, Guofeng
Chen, Haibo
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2017, 54 (03) : 895 - 909
[5] Infinitely Many Homoclinic Solutions for Fourth Order p-Laplacian Differential Equations
Tersian, Stepan
[J]. MATHEMATICS, 2020, 8 (04)
[6] Infinitely many high energy solutions for fourth-order ellip- tic equations with p-Laplacian in bounded domain
Chahma, Youssouf
Chen, Haibo
[J]. JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2024, 32 (02): : 109 - 121
[7] Existence of infinitely many solutions for p-Laplacian equations in RN
Lin, Xiaoyan
Tang, X. H.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 92 : 72 - 81
[8] Infinitely many solutions for a class of fourth order elliptic equations in RN
Yang, Min Bo
Shen, Zi Fei
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2008, 24 (08) : 1269 - 1278
[9] Infinitely many solutions for a class of fourth order elliptic equations in RN
Min Bo Yang
Zi Fei Shen
[J]. Acta Mathematica Sinica, English Series, 2008, 24 : 1269 - 1278
[10] Multiplicity of Solutions for Fourth-Order Elliptic Equations with p-Laplacian and Mixed Nonlinearity
Benhanna, A. H.
Choutri, A.
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2020, 17 (02)

← 1 2 3 4 5 →