Abstract In this paper we consider the Henon problem in the unit disc with Dirichlet boundary conditions. We study the asymptotic profile of least energy and nodal least energy radial solutions and then deduce the exact computation of their Morse index for large values of the exponent p. As a consequence of this computation a multiplicity result for positive and nodal solutions is obtained.

中文翻译：

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盘中指数大的 Hénon 问题

摘要 本文考虑具有Dirichlet 边界条件的单位圆盘中的Henon 问题。我们研究了最小能量和节点最小能量径向解的渐近曲线，然后推导出它们的莫尔斯指数对于指数 p 的大值的精确计算。作为该计算的结果，获得了正解和节点解的多重结果。