Nonradial solutions of a nonhomogeneous semilinear elliptic problem with linear growth

In this paper we consider the problem−Δu=bu+−φ1in B,u=0on ∂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.