Multiplicity results for solutions of p-biharmonic problems

被引：5

作者：

Lu, Yao ^{[1
]}

Fu, Yongqiang ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 190卷

基金：

中国国家自然科学基金;

关键词：

p-biharmonic operator; Cohomological linking; Fountain theorem over cones; Critical nonlinearity; BIFURCATION; EIGENVALUE; EQUATIONS;

D O I：

10.1016/j.na.2019.111596

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we deal with the multiplicity existence of solutions for the following p-biharmonic equation: { Delta(2)(p)u = lambda vertical bar u vertical bar(p-2)u + vertical bar u vertical bar(q-2)u, in Omega, u = Delta u = 0, on partial derivative Omega, where Omega is a bounded domain in R-N, Delta(2)(p)u = Delta(vertical bar Delta u vertical bar(p-2) Delta u), p < q <= p* = N-p/N-2p, lambda is an element of R is a parameter. When p < q < p*, we prove that the above problem possesses infinitely many solutions. While when q = p*, a multiplicity existence result is obtained. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页数：13

共 19 条

[1] ADAMS R. A., 2003, SOBOLEV SPACES
[2] [Anonymous], 2010, Morse Theoretic Aspects of p-Laplacian Type Operators. Mathematical surveys and monographs
[3] [Anonymous], COMMUN APPL ANAL
[4] [Anonymous], 2003, Topol. Methods Nonlinear Anal.
[5] Estimates of the principal eigenvalue of the p-biharmonic operator
Benedikt, Jiri
Drabek, Pavel
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (13) : 5374 - 5379
[6] Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations
Chen, Y
McKenna, PJ
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 136 (02) : 325 - 355
[7] Multiplicity of solutions for p(x)-polyharmonic elliptic Kirchhoff equations
Colasuonno, Francesca
Pucci, Patrizia
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (17) : 5962 - 5974
[8] GENERALIZED CO-HOMOLOGICAL INDEX THEORIES FOR LIE GROUP ACTIONS WITH AN APPLICATION TO BIFURCATION QUESTIONS FOR HAMILTONIAN SYSTEMS
FADELL, ER
RABINOWITZ, PH
[J]. INVENTIONES MATHEMATICAE, 1978, 45 (02) : 139 - 174
[9] Multiplicity of positive radially symmetric solutions for a quasilinear biharmonic equation in the plane
Guo, Zhichang
Yin, Jingxue
Ke, Yuanyuan
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (04) : 1320 - 1330
[10] Sign-changing solutions for p-biharmonic equations with Hardy potential
Huang, Yisheng
Liu, Xiangqing
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 412 (01) : 142 - 154

← 1 2 →