Nonradial solutions of a nonhomogeneous semilinear elliptic problem with linear growth

In this paper we consider the problem -Delta u = bu(+) - phi(1) in B, u = 0 on partial derivative B and prove that a mountain pass solution is nonradial if the parameter b is sufficiently large. The proof is based on showing that the linearized operator at a radial solution has many negative eigenvalues, while in the case of a mountain pass solution it can have at most one negative eigenvalue. This approach works even if the functional corresponding to the problem is not twice differentiable. (c) 2007 Elsevier Inc. All rights reserved.