A BIHARMONIC EIGENVALUE PROBLEM AND ITS APPLICATION

doi:10.1016/S0252-9602(12)60093-9

Abstract

Abstract:

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(R^N), 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 R^N.

Key words: Biharmonic equation, potential well, eigenvalue problem, asymptotically lin-ear

CLC Number:

35J20

WANG Jiang-Chao, ZHANG Yi-Min. A BIHARMONIC EIGENVALUE PROBLEM AND ITS APPLICATION[J].Acta mathematica scientia,Series B, 2012, 32(3): 1213-1225.

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