Positive solutions of biharmonic elliptic problems with a parameter

被引：2

作者：

Chen, Haiping ^{[1
]}

Feng, Meiqiang ^{[1
]}

机构：

[1] Beijing Informat Sci & Technol Univ, Sch Appl Sci, Beijing 100192, Peoples R China

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2024年 / 14卷 / 01期

基金：

中国国家自然科学基金; 北京市自然科学基金;

关键词：

Singular biharmonic equation; Navier boundary conditions; Positive solution; Existence; Nonexistence and multiplicity; Fixed point theory; SIGN-CHANGING SOLUTIONS; NONTRIVIAL SOLUTIONS; EXISTENCE; EQUATIONS; UNIQUENESS; MULTIPLICITY; THEOREMS;

D O I：

10.1007/s13324-023-00860-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we analyze the existence, multiplicity and nonexistence of positive solutions for a class of biharmonic equations with Navier boundary conditions and a parameter. In addition, some new criteria for the existence, multiplicity and nonexistence of positive radial solutions for a singular biharmonic equation are also investigated. Our approaches use fixed point theorems on cones.

引用

页数：36

共 53 条

[1]

Abid I, 2008, DIFFER INTEGRAL EQU, V21, P653

[2] FIXED-POINT EQUATIONS AND NONLINEAR EIGENVALUE PROBLEMS IN ORDERED BANACH-SPACES [J].

AMANN, H .

SIAM REVIEW, 1976, 18 (04) :620-709

[3] A semilinear fourth order elliptic problem with exponential nonlinearity [J].

Arioli, G ;

Gazzola, F ;

Grunau, HC ;

Mitidieri, E .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 36 (04) :1226-1258

[4] Asymptotic proximity to higher order nonlinear differential equations [J].

Astashova, Irina ;

Bartusek, Miroslav ;

Dosla, Zuzana ;

Marini, Mauro .

ADVANCES IN NONLINEAR ANALYSIS, 2022, 11 (01) :1598-1613

[5] NONNEGATIVE SOLUTIONS FOR A CLASS OF SEMIPOSITONE NONLINEAR ELLIPTIC EQUATIONS IN BOUNDED DOMAINS OF Rn [J].

Bachar, Imed ;

Maagli, Habib ;

Eltayeb, Hassan .

OPUSCULA MATHEMATICA, 2022, 42 (06) :793-803

[6] A note on a class of higher order conformally covariant equations [J].

Chang, SYA ;

Chen, WX .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2001, 7 (02) :275-281

[7] Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations [J].

Chen, Y ;

McKenna, PJ .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 136 (02) :325-355

[8] POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC-SYSTEMS [J].

CLEMENT, P ;

DEFIGUEIREDO, DG ;

MITIDIERI, E .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1992, 17 (5-6) :923-940

[9] Neumann Eigenvalues of the Biharmonic Operator on Domains: Geometric Bounds and Related Results [J].

Colbois, Bruno ;

Provenzano, Luigi .

JOURNAL OF GEOMETRIC ANALYSIS, 2022, 32 (08)

[10] A COMPARISON PRINCIPLE FOR A CLASS OF 4TH-ORDER ELLIPTIC-OPERATORS [J].

COSNER, C ;

SCHAEFER, PW .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1987, 128 (02) :488-494

← 1 2 3 4 5 6 →