BLOWING UP AND MULTIPLICITY OF SOLUTIONS FOR A FOURTH-ORDER EQUATION WITH CRITICAL NONLINEARITY

被引：0

作者：

Siwar AMMAR ^{[1
]}

Mokhles HAMMAMI ^{[2
]}

机构：

[1] Department of mathematics, University of Monastir

[2] Department of mathematics, Faculty of Sciences of sfax, University of Sfax

来源：

Acta Mathematica Scientia | 2015年 / 35卷 / 06期

关键词：

fourth order elliptic equations; critical Sobolev exponent; blow up solution;

D O I：

暂无

中图分类号：

O175.25 [椭圆型方程];

学科分类号：

070104 ;

摘要：

In this paper,we consider the following nonlinear elliptic problem:△2u=|u|(8/(n-4))u+μ|u|q-1u,in Ω,△u = u = 0 on δΩ,where Ω is a bounded and smooth domain in Rn,n ∈ {5,6,7},μ is a parameter and q ∈]4/(n- 4),(12- n)/(n- 4)[.We study the solutions which concentrate around two points of Ω.We prove that the concentration speeds are the same order and the distances of the concentration points from each other and from the boundary are bounded.For Ω =(Ωα)α a smooth ringshaped open set,we establish the existence of positive solutions which concentrate at two points of Ω.Finally,we show that for μ > 0,large enough,the problem has at least many positive solutions as the LjusternikSchnirelman category of Ω.

引用

页码：1511 / 1546

页数：36

共 50 条

[21] High energy solutions for the fourth-order elliptic equations in RN [J].

Cheng, Bitao .

BOUNDARY VALUE PROBLEMS, 2014, :1-11

[22] EXISTENCE AND CONCENTRATION OF SOLUTIONS FOR SUBLINEAR FOURTH-ORDER ELLIPTIC EQUATIONS [J].

Zhang, Wen ;

Tang, Xianhua ;

Zhang, Jian .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,

[23] B-method approach to blow-up solutions of fourth-order semilinear parabolic equations [J].

Huo, Guanze ;

Zou, Yongkui ;

Xu, Yingxiang .

NUMERICAL ALGORITHMS, 2020, 85 (04) :1365-1384

[24] B-method approach to blow-up solutions of fourth-order semilinear parabolic equations [J].

Guanze Huo ;

Yongkui Zou ;

Yingxiang Xu .

Numerical Algorithms, 2020, 85 :1365-1384

[25] On a fourth-order quasilinear elliptic equation of concave-convex type [J].

dos Santos, Ederson Moreira .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2009, 16 (03) :297-326

[26] MULTIPLICITY OF POSITIVE SOLUTIONS FOR FRACTIONAL LAPLACIAN EQUATIONS INVOLVING CRITICAL NONLINEARITY [J].

Zhang, Jinguo ;

Liu, Xiaochun ;

Mao, Hongying .

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2019, 53 (01) :151-182

[27] Existence and multiplicity of solutions to elliptic equations of fourth order on compact manifolds [J].

Benalili, Mohammed .

DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 2009, 6 (03) :203-225

[28] Nonexistence of bounded energy solutions for a fourth order equation on thin annuli [J].

Ayeda, MB ;

El Mehdi, K ;

Hammami, M .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2004, 3 (04) :557-580

[29] EXISTENCE OF THREE NONTRIVIAL SOLUTIONS FOR A CLASS OF FOURTH-ORDER ELLIPTIC EQUATIONS [J].

Li, Chun ;

Agarwal, Ravi P. ;

Ou, Zeng-Qi .

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2018, 51 (02) :331-344

[30] AN EIGENVALUE PROBLEM RELATED TO BLOWING-UP SOLUTIONS FOR A SEMILINEAR ELLIPTIC EQUATION WITH THE CRITICAL SOBOLEV EXPONENT [J].

Takahashi, Futoshi .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2011, 4 (04) :907-922

← 1 2 3 4 5 →