On some fourth-order semilinear elliptic problems in RN

被引：71

作者：

Chabrowski, J

do O, JM ^{[1
]}

机构：

[1] Univ Fed Paraiba, Dept Matemat, CCEN, BR-58059900 Joao Pessoa, Paraiba, Brazil

[2] Univ Queensland, Dept Math, St Lucia, Qld 4072, Australia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2002年 / 49卷 / 06期

关键词：

biharmonic operator; principal eigenvalue; mountain-pass theorem; constrained minimization; critical growth;

D O I：

10.1016/S0362-546X(01)00144-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The existence of two solutions for a fourth-order semilinear elliptic problem involving critical growth from the viewpoint of Sobolev embedding was established. The basic tools used in the analysis were the mountain-pass theorem, constrained minimization, and concentration-compactness principle. The existence of positive principle eigenvalues for the corresponding linear elliptic problem was also investigated.

引用

页码：861 / 884

页数：24

共 50 条

[1] Nontrivial solutions for some fourth order semilinear elliptic problems
Micheletti, AM
Pistoia, A
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 34 (04) : 509 - 523
[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 of nontrivial solution for fourth-order semilinear Δγ-Laplace equation RN
Duong Trong Luyen
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2019, (78) : 1 - 12
[4] Fourth-order elliptic problems with critical nonlinearities by a sublinear perturbation
Li, Lin
O'Regan, Donal
NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2021, 26 (02): : 227 - 240
[5] Multiplicity results for some fourth-order elliptic equations
Wei, Yuanhong
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 385 (02) : 797 - 807
[6] Existence results for some fourth-order nonlinear elliptic problems of local superlinearity and sublinearity
Xu, GX
Zhang, JH
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 281 (02) : 633 - 640
[7] Non-uniformly asymptotically linear fourth-order elliptic problems
Pei, Ruichang
Zhang, Jihui
BOUNDARY VALUE PROBLEMS, 2015, : 1 - 14
[8] POSITIVITY FOR FOURTH-ORDER SEMILINEAR PROBLEMS RELATED TO THE KIRCHHOFF-LOVE FUNCTIONAL
Romani, Giulio
ANALYSIS & PDE, 2017, 10 (04): : 943 - 982
[9] Non-uniformly asymptotically linear fourth-order elliptic problems
Ruichang Pei
Jihui Zhang
Boundary Value Problems, 2015
[10] CONCENTRATION PHENOMENA FOR A FOURTH-ORDER EQUATION ON Rn
Ben Ayed, Mohamed
Selmi, Abdelbaki
PACIFIC JOURNAL OF MATHEMATICS, 2009, 242 (01) : 1 - 32

← 1 2 3 4 5 →