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