AI 中文总结
本文研究三维Allen-Cahn方程有界整体解，证明有限Morse指标I的解至多有2I个端，并推广了指标1解轴对称的早期结果。
AI 中文摘要
我们研究三维空间中具有二次能量增长的Allen-Cahn方程的有界整体解。我们证明了具有有限Morse指标I的此类解至多有2I个端。此外，我们证明了Morse指标为1的解有两个端并且是轴对称的，这推广了Florit-Simon的一个早期结果。
英文摘要
We study bounded entire solutions of the Allen-Cahn equation in dimension three with quadratic energy growth. We prove that such a solution of finite Morse index I has at most 2I ends. Furthermore, we show that Morse index one solutions have two ends and are axially symmetric, which generalizes an earlier result by Florit-Simon.
