Existence and multiplicity of solutions for nonlocal fourth-order elliptic equations with combined nonlinearities

被引：1

作者：

Yuanfang, Ru ^{[1
]}

Yukun, An ^{[2
]}

机构：

[1] China Pharmaceut Univ, Coll Sci, Nanjing 211198, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Coll Sci, Nanjing 210016, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2020年 / 2020卷 / 01期

关键词：

Fourth-order elliptic equation; Nonlocal; Asymptotically linear; Mountain pass theorem; Critical point; KIRCHHOFF-TYPE; NONTRIVIAL SOLUTIONS; POSITIVE SOLUTIONS;

D O I：

10.1186/s13661-020-01430-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the following nonlocal fourth-order elliptic problem: {Delta(2)u-m(integral(Omega)vertical bar del u vertical bar(2)dx)Delta u = a(x)vertical bar u vertical bar(s) (2)u+f(x, u), x is an element of Omega, u - Delta u = 0, x is an element of partial derivative Omega, by using the mountain pass theorem, the least action principle, and the Ekeland variational principle, the existence and multiplicity results are obtained.

引用

页数：16

共 50 条

[1] Existence and multiplicity of solutions for nonlocal fourth-order elliptic equations with combined nonlinearities
Ru Yuanfang
An Yukun
Boundary Value Problems, 2020
[2] Existence and multiplicity of solutions for fourth-order elliptic equations in RN
Ye, Yiwei
Tang, Chun-Lei
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 406 (01) : 335 - 351
[3] Existence and multiplicity of weak solutions for a system of fourth-order elliptic equations with combined nonlocal and indefinite source terms
Kefi, Khaled
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2025, 48 (01) : 517 - 534
[4] Multiplicity results for some fourth-order elliptic equations with combined nonlinearities
Pei, Ruichang
Xia, Hongming
AIMS MATHEMATICS, 2023, 8 (06): : 14704 - 14725
[5] Existence and multiplicity of solutions for a class of fourth-order elliptic equations in RN
Liu, Jiu
Chen, ShaoXiong
Wu, Xian
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 395 (02) : 608 - 615
[6] Existence and Multiplicity of Nontrivial Solutions for a Class of Fourth-Order Elliptic Equations
Li, Chun
Ou, Zeng-Qi
Tang, Chun-Lei
ABSTRACT AND APPLIED ANALYSIS, 2013,
[7] Existence and multiplicity of solutions for a fourth-order elliptic equation
Wang, Fanglei
An, Yukun
BOUNDARY VALUE PROBLEMS, 2012,
[8] Existence and multiplicity of solutions for a fourth-order elliptic equation
Fanglei Wang
Yukun An
Boundary Value Problems, 2012
[9] Existence and multiplicity of solutions for fourth-order elliptic Kirchhoff equations with potential term
Ansari, Hajar
Vaezpour, Seyed Mansour
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2015, 60 (05) : 668 - 695
[10] Existence and multiplicity of positive solutions for a fourth-order elliptic equation
Figueiredo, Giovany M.
Furtado, Marcelo F.
da Silva, Joao Pablo P.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2020, 150 (02) : 1053 - 1069

← 1 2 3 4 5 →