The Hénon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore, it has asymmetric solutions on a symmetric domain even though the Emden equation has no asymmetric unidirectional solution on such a domain. We discuss a numerical verification method for proving the existence of solutions of the Hénon equation on a bounded domain. By applying the method to a line-segment domain and a square domain, we numerically prove the existence of solutions of the Hénon equation for several parameters representing the ratio of transverse to radial velocity. As a result, we find a set of undiscovered solutions with three peaks on the square domain.

Hénon 方程是 Emden 方程的一种广义形式，它允许在横向速度与径向速度的某个比率下发生对称破坏分岔。因此，即使 Emden 方程在对称域上没有非对称单向解，它在对称域上也有非对称解。我们讨论了一种数值验证方法，用于证明 Hénon 方程在有界域上的解的存在性。通过将该方法应用于线段域和方形域，我们数值证明了 Hénon 方程对于表示横向与径向速度比的几个参数的解的存在性。结果，我们找到了一组未发现的解，在方形域上有三个峰值。