Abstract
In this paper, we study the generalized Hénon equation with a radial coefficient function in the unit ball and show the existence of a positive non-radial solution. Our result is applicable to a wide class of coefficient functions. Our theorem ensures that if the ratio of the density of the coefficient function in | x | < a to that in a < | x | < 1 is small enough and a is sufficiently close to 1, then a least energy solution is not radially symmetric.
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