Bifurcation and multiplicity results for fourth-order equations

被引：2

作者：

Lu, Yao ^{[1
]}

Fu, Yongqiang ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin, Heilongjiang, Peoples R China

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2019年 / 64卷 / 10期

关键词：

Biharmonic operator; eigenvalue; bifurcation; minimax method; NONTRIVIAL SOLUTIONS;

D O I：

10.1080/17476933.2018.1536700

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove that fourth-order equations involving biharmonic operator with superlinear growth at infinity and saddle structure near zero have three nontrivial solutions. The approach is based on a combination of bifurcation theory and minimax methods.

引用

页码：1617 / 1633

页数：17

共 50 条

[31] Positive supersolutions of fourth-order nonlinear elliptic equations: explicit estimates and Liouville theorems [J].

Aghajani, Asadollah ;

Cowan, Craig ;

Radulescu, Vicentiu D. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 298 :323-345

[32] Existence of solutions for some fourth-order nonlinear elliptic problems [J].

Yang, Yang ;

Zhang, Jihui .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 351 (01) :128-137

[33] Multiple Solutions for Critical Fourth-Order Elliptic Equations of Kirchhoff type [J].

Fu Zhao ;

Zeyi Liu ;

Sihua Liang .

Bulletin of the Malaysian Mathematical Sciences Society, 2021, 44 :1057-1064

[34] Infinitely many solutions for fourth-order elliptic equations with general potentials [J].

Zhang, Wen ;

Tang, Xianhua ;

Zhang, Jian .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 407 (02) :359-368

[35] Multiple solutions for a class of nonhomogeneous fourth-order quasilinear equations with nonlinearities [J].

Almuaalemi, Belal ;

Chen, Haibo ;

Khoutir, Sofiane .

DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2022, 30 (03) :573-583

[36] On Fourth-Order Elliptic Equations of Kirchhoff Type with Dependence on the Gradient and the Laplacian [J].

Ru, Yuanfang ;

Wang, Fanglei ;

Wang, Yunhai ;

An, Tianqing .

JOURNAL OF FUNCTION SPACES, 2018, 2018

[37] Ground states for a class of asymptotically linear fourth-order elliptic equations [J].

Zhang, Wen ;

Tang, Xianhua ;

Zhang, Jian .

APPLICABLE ANALYSIS, 2015, 94 (10) :2168-2174

[38] Multiple Solutions for Critical Fourth-Order Elliptic Equations of Kirchhoff type [J].

Zhao, Fu ;

Liu, Zeyi ;

Liang, Sihua .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2021, 44 (02) :1057-1064

[39] Numerical methods for fourth-order elliptic equations with nonlocal boundary conditions [J].

Pao, C. V. ;

Wang, Yuan-Ming .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 292 :447-468

[40] Multiple solutions for a class of fourth-order elliptic equations with critical growth [J].

Tian, Guaiqi ;

Lei, Jun ;

An, Yucheng .

OPEN MATHEMATICS, 2025, 23 (01)

← 1 2 3 4 5 →