Liouville theorems for stable solutions of biharmonic problem

Abstract

We prove some Liouville type results for stable solutions to the biharmonic problem ∆u = u, u > 0 in R where 1 < q < ∞. For example, for n ≥ 5, we show that there are no stable classical solution in R when n+4 n−4 < q ≤ ( n−8 n )−1 + .

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Cite this paper

@inproceedings{Wei2012LiouvilleTF, title={Liouville theorems for stable solutions of biharmonic problem}, author={Juncheng Wei and Dong Ye}, year={2012} }