Acta mathematica scientia, Series B >
A BIHARMONIC EIGENVALUE PROBLEM AND ITS APPLICATION
Received date: 2011-01-13
Online published: 2012-05-20
Supported by
Project supported by the National Science Foundation of China (11071245). †Corresponding author.
In this article, we focus on the eigenvalue problem of the following linear biharmonic equation in RN:
△2u−αu+λg(x)u = 0 with u ∈ H2(RN), u ≠0, N ≥ 5. (*)
Note that there are two parameters and α in it, which is different from the usual eigen-value problems. Here, we consider λ as an eigenvalue and seek for a suitable 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 so-lutions, 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 RN.
WANG Jiang-Chao , ZHANG Yi-Min . A BIHARMONIC EIGENVALUE PROBLEM AND ITS APPLICATION[J]. Acta mathematica scientia, Series B, 2012 , 32(3) : 1213 -1225 . DOI: 10.1016/S0252-9602(12)60093-9
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