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

Axially symmetric solutions of Allen-Cahn equation with finite Morse index