Multiplicity of positive and nodal solutions for nonlinear elliptic problems in RN

We consider the following problem: [GRAPHICS] where 2 < p < 2N/N-2, N greater than or equal to 3, mu > 0, Q(x) is an element of C(R-N) and Q(x) greater than or equal to 0 for x is an element of R-N, f(x, t), f(t)(x, t) is an element of C(R-N x R), f(x, t) greater than or equal to 0 for all x is an element of R-N and t is an element of R+, f(x, t) is an odd function of t. We show that if the maximum of Q(x) is achieved at k different points of R-N, then for mu large enough the above problem has at least k positive solutions and k nodal solutions.