A BIHARMONIC EIGENVALUE PROBLEM AND ITS APPLICATION

In this article, we focus on the eigenvalue problem of the following linear biharmonic equation in R^N： △^2u-αu＋λg（x）u=0 with u ∈H^2（R^N）,u≠0,N≥5 Note that there are two parameters α and λ in it, which is different from the usual eigenvalue problems. Here, we consider λ as an eigenvalue and seek Ior...

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Bibliographic Details
Published inActa mathematica scientia Vol. 32; no. 3; pp. 1213 - 1225
Main Author 王江潮 张贻民
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.05.2012
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
Subjects
35J20
35J60
asymptotically linear
Biharmonic equation
Biharmonic equations
eigenvalue problem
Eigenvalues
IOR
potential well
双调和方程
应用
损失
最大值原理
渐近线性
特征值问题
非平凡解
potential well
Biharmonic equation
35J20
asymptotically linear
35J60
eigenvalue problem
Online AccessGet full text
ISSN0252-9602
1572-9087
DOI10.1016/S0252-9602(12)60093-9

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Summary:In this article, we focus on the eigenvalue problem of the following linear biharmonic equation in R^N： △^2u-αu＋λg（x）u=0 with u ∈H^2（R^N）,u≠0,N≥5 Note that there are two parameters α and λ in it, which is different from the usual eigenvalue problems. Here, we consider λ as an eigenvalue and seek Ior a sulble range of parameter α, which ensures that problem （＊） has a maximal eigenvalue. As the loss of strong maximum principle for our problem, we can only get the existence of non-trivial solutions, not positive solutions, in this article. As an application, by using these results, we studied also the existence of non-trivial solutions for an asymptotically linear biharmonic equation in R^N.
Bibliography:In this article, we focus on the eigenvalue problem of the following linear biharmonic equation in R^N： △^2u-αu＋λg（x）u=0 with u ∈H^2（R^N）,u≠0,N≥5 Note that there are two parameters α and λ in it, which is different from the usual eigenvalue problems. Here, we consider λ as an eigenvalue and seek Ior a sulble range of parameter α, which ensures that problem （＊） has a maximal eigenvalue. As the loss of strong maximum principle for our problem, we can only get the existence of non-trivial solutions, not positive solutions, in this article. As an application, by using these results, we studied also the existence of non-trivial solutions for an asymptotically linear biharmonic equation in R^N.
42-1227/O
Biharmonic equation; potential well; eigenvalue problem; asymptotically linear
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(12)60093-9