In this paper, we deal with a class of fractional Hénon equation and by using the Lyapunov-Schmidt reduction method, under some suitable assumptions, we derive the existence of infinitely many solutions, whose energy can be made arbitrarily large. Compared to the previous works, we encounter some new challenges because of the nonlocal property for fractional Laplacian. But by doing some delicate estimates for the nonlocal term we overcome the difficulty and find infinitely many nonradial solutions.

中文翻译：

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一个非局部问题的无限多个解的存在

在本文中，我们处理了一类分数阶Hénon方程，并使用Lyapunov-Schmidt约简方法，在适当的假设下，得出存在无穷多个解的存在，其能量可以任意增大。与以前的作品相比，由于分数拉普拉斯算子的非局部性质，我们遇到了一些新的挑战。但是通过对非局部项进行一些精细的估计，我们克服了困难并找到了无数个非径向解。