【摘 要】
：
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
【机 构】
：
Wuhan Institute of Physics and Mathematics
【基金项目】
：
the National Science Foundation of China
论文部分内容阅读
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 α and λ in it,which is different from the usual eigenvalue 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 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 RN.
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