On the Lane-Emden conjecture

Kui Li; Zhitao Zhang

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arXiv · 1807.06751

On the Lane-Emden conjecture

Kui Li·Zhitao Zhang

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Abstract

We consider the Lane-Emden conjecture which states that there is no non-trivial non-negative solution for the Lane-Emden system whenever the pair of exponents is subcritical. By Sobolev embeddings on $S^{N-1}$ and scale invariance of the solutions, we show this conjecture holds in a new region. Our methods can also be used to prove the Lane-Emden conjecture in space dimension $N\leq 4$, that is to give a different proof of the main result of Souplet in Adv. Math. 2009.

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Kui Li, Zhitao Zhang. 2018-07-18. On the Lane-Emden conjecture. https://arxiv.org/abs/1807.06751

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