EXISTENCE AND CONCENTRATION OF SOLUTIONS FOR SUBLINEAR FOURTH-ORDER ELLIPTIC EQUATIONS

被引：0

作者：

Zhang, Wen ^{[1
]}

Tang, Xianhua ^{[1
]}

Zhang, Jian ^{[1
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年

关键词：

Fourth-order elliptic equations; variational method; concentration; NONTRIVIAL SOLUTIONS; SCHRODINGER-EQUATIONS; MULTIPLICITY;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article concerns the fourth-order elliptic equations Delta(2)u - Delta u + lambda V(x)u = f (x, u), x (sic) R-N, u (sic) H-2(R-N), where lambda > 0 is a parameter, V (sic) C(R-N) and V-1(0) has nonempty interior. Under some mild assumptions, we establish the existence of nontrivial solutions. Moreover, the concentration of solutions is also explored on the set V-1(0) as lambda -> infinity.

引用

页数：9

共 34 条

[1]

Alexiades V., 1980, Nonlinear Analysis Theory, Methods & Applications, V4, P805, DOI 10.1016/0362-546X(80)90080-2

[2] Existence of nontrivial solutions of an asymptotically linear fourth-order elliptic equation [J].

An, Yukun ;

Liu, Renyi .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (11) :3325-3331

[3]

[Anonymous], 1996, Minimax Theorems, DOI DOI 10.1007/978

[4] Nonlinear Schrodinger equations with steep potential well [J].

Bartsch, T ;

Pankov, A ;

Wang, ZQ .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2001, 3 (04) :549-569

[5] EXISTENCE AND MULTIPLICITY RESULTS FOR SOME SUPERLINEAR ELLIPTIC PROBLEMS ON R(N) [J].

BARTSCH, T ;

WANG, ZQ .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1995, 20 (9-10) :1725-1741

[6] On a fourth order elliptic equation with critical nonlinearity in dimension six [J].

Ben Ayed, M ;

Hammami, M .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (05) :924-957

[7] Multiplicity of solutions for a fourth order elliptic equation with critical exponent on compact manifolds [J].

Benalili, Mohammed .

APPLIED MATHEMATICS LETTERS, 2007, 20 (02) :232-237

[8] 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

[9] LARGE-AMPLITUDE PERIODIC OSCILLATIONS IN SUSPENSION BRIDGES - SOME NEW CONNECTIONS WITH NONLINEAR-ANALYSIS [J].

LAZER, AC ;

MCKENNA, PJ .

SIAM REVIEW, 1990, 32 (04) :537-578

[10] Semiclassical solutions of perturbed p-Laplacian equations with critical nonlinearity [J].

Lin, Xiaoyan ;

Tang, X. H. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 413 (01) :438-449

← 1 2 3 4 →