Two solutions for an elliptic problem with two singular terms

We study the Dirichlet boundary value problem with 0-boundary data for the semilinear elliptic equation-Delta = (lambda u(s-1)- u(r-1))x{u> 0} in a bounded domain Omega,where0 < r < s < 1 and lambda is an element of (0 infinity()). In particular, for. large enough, we prove the existence of at least two nonnegative solutions, one of which is positive, satisfies the Hopf's boundary condition and corresponds to a local minimum of the energy functional. This paper is motivated by a recent result of the authors where the same conclusion was obtained for the case 0 < r = 1 < s < 2.