Non-radial least energy solutions of the generalized Henon equation

In this paper, we study the generalized Henon 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 vertical bar x vertical bar < a to that in a < vertical bar x vertical bar < 1 is small enough and a is sufficiently close to 1, then a least energy solution is not radially symmetric. (C) 2011 Elsevier Inc. All rights reserved.