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Axially symmetric solutions of Allen-Cahn equation with finite Morse index. (arXiv:1901.11263v1 [math.AP])

In this paper we study axially symmetric solutions of Allen-Cahn equation with finite Morse index. It is shown that there does not exist such a solution in dimensions between $4$ and $10$. In dimension $3$, we prove that these solutions have finitely many ends. Furthermore, the solution has exactly two ends if its Morse index equals $1$.查看全文

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