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
An, Yukun
Liu, Renyi
[J]. 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
Bartsch, T
Pankov, A
Wang, ZQ
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2001, 3 (04) : 549 - 569
[5] EXISTENCE AND MULTIPLICITY RESULTS FOR SOME SUPERLINEAR ELLIPTIC PROBLEMS ON R(N)
BARTSCH, T
WANG, ZQ
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1995, 20 (9-10) : 1725 - 1741
[6] On a fourth order elliptic equation with critical nonlinearity in dimension six
Ben Ayed, M
Hammami, M
[J]. 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
Benalili, Mohammed
[J]. APPLIED MATHEMATICS LETTERS, 2007, 20 (02) : 232 - 237
[8] 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
[9] LARGE-AMPLITUDE PERIODIC OSCILLATIONS IN SUSPENSION BRIDGES - SOME NEW CONNECTIONS WITH NONLINEAR-ANALYSIS
LAZER, AC
MCKENNA, PJ
[J]. SIAM REVIEW, 1990, 32 (04) : 537 - 578
[10] Semiclassical solutions of perturbed p-Laplacian equations with critical nonlinearity
Lin, Xiaoyan
Tang, X. H.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 413 (01) : 438 - 449

← 1 2 3 4 →