In this paper we provide a numerical approximation of bifurcation branches from nodal radial solutions of the Lane Emden Dirichlet problem in the unit ball in ℝ 2 , as the exponent of the nonlinearity varies. We consider solutions with two or three nodal regions. In the first case our numerical results complement the analytical ones recently obtained in [11]. In the case of solutions with three nodal regions, for which no analytical results are available, our analysis gives numerical evidence of the existence of bifurcation branches. We also compute additional approximations indicating presence of an unexpected branch of solutions with six nodal regions. In all cases the numerical results allow to formulate interesting conjectures.

中文翻译：

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球中 Lane-Emden 问题的近似非径向解

在本文中，我们在 ℝ 2 中的单位球中提供了来自 Lane Emden Dirichlet 问题的节点径向解的分岔分支的数值近似，因为非线性的指数会发生变化。我们考虑具有两个或三个节点区域的解决方案。在第一种情况下，我们的数值结果补充了最近在 [11] 中获得的分析结果。在具有三个节点区域的解的情况下，没有可用的分析结果，我们的分析给出了分叉分支存在的数值证据。我们还计算了额外的近似值，表明存在具有六个节点区域的意外分支解决方案。在所有情况下，数值结果都允许提出有趣的猜想。