NONRADIAL SOLUTIONS OF A NEUMANN HENON EQUATION ON A BALL

In this work we examine the existence of positive classical solutions of {-Delta+u = vertical bar x vertical bar(alpha)u(p-1) in B-1, u > 0 in B-1, partial derivative(nu)u = 0 on partial derivative B-1, where p > 1, alpha > 0 and B-1 is the unit ball in R-N where N >= 4 and is even. Of particular interest is the existence of nonradial position classical solutions. We show that under suitable conditions on p ,alpha and N there are positive classical nonradial solutions. Our approach is to utilize a variational approach on suitable convex cones.