MULTIPLE SOLUTIONS FOR A CLASS OF MODIFIED QUASILINEAR FOURTH-ORDER ELLIPTIC EQUATIONS

被引：0

作者：

Wu, Zijian ^{[1
]}

Chen, Haibo ^{[1
]}

机构：

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

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2022年 / 12卷 / 05期

关键词：

Fourth-order elliptic equations; multiple solutions; Mountain Pass lemma; local minimization; SCHRODINGER-EQUATIONS; NONTRIVIAL SOLUTIONS; POSITIVE SOLUTIONS; SOLITON-SOLUTIONS; KIRCHHOFF TYPE; EXISTENCE;

D O I：

10.11948/20210401

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the following modified quasilinear fourthorder elliptic equations:. Delta(2)u - (a + b integral(R3) |del u|(2) dx)Delta u + V (x)u -k/2 Delta(u(2))u = f(x, u), in R-3, where a > 0, b >= 0, >= 0. Under some appropriate assumptions on V (x) and f(x, u), multiplicity results of two different type of solutions are established via the Mountain Pass lemma and the local minimization. Keywords Fourth-order elliptic equations, multiple solutions, Mountain Pass lemma, local minimization.

引用

页码：1945 / 1958

页数：14

共 50 条

[1] Multiple solutions for a class of nonhomogeneous fourth-order quasilinear equations with nonlinearities
Belal Almuaalemi
Haibo Chen
Sofiane Khoutir
[J]. Differential Equations and Dynamical Systems, 2022, 30 : 573 - 583
[2] Multiple solutions for a class of nonhomogeneous fourth-order quasilinear equations with nonlinearities
Almuaalemi, Belal
Chen, Haibo
Khoutir, Sofiane
[J]. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2022, 30 (03) : 573 - 583
[3] High energy solutions of modified quasilinear fourth-order elliptic equation
Xiujuan Wang
Anmin Mao
Aixia Qian
[J]. Boundary Value Problems, 2018
[4] High energy solutions of modified quasilinear fourth-order elliptic equation
Wang, Xiujuan
Mao, Anmin
Qian, Aixia
[J]. BOUNDARY VALUE PROBLEMS, 2018,
[5] Multiple nontrivial solutions for some fourth-order quasilinear elliptic problems
Zhang, Jihui
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (5-7) : E2533 - E2544
[6] 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
[7] High energy solutions of modified quasilinear fourth-order elliptic equations with sign-changing potential
Cheng, Bitao
Tang, Xianhua
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (01) : 27 - 36
[8] A class of modified nonlinear fourth-order elliptic equations with unbounded potential
Oliveira Junior, J. C.
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2021, 66 (05) : 876 - 891
[9] EXISTENCE OF THREE NONTRIVIAL SOLUTIONS FOR A CLASS OF FOURTH-ORDER ELLIPTIC EQUATIONS
Li, Chun
Agarwal, Ravi P.
Ou, Zeng-Qi
[J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2018, 51 (02) : 331 - 344
[10] Existence and multiplicity of nontrivial solutions for a class of modified nonlinear fourth-order elliptic equations on RN
Chen, Shaoxiong
Liu, Jiu
Wu, Xian
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 248 : 593 - 601

← 1 2 3 4 5 →