Two Infinite Families of Solutions for Singular Superlinear Equations on Exterior Domains

In this paper, we study radial solutions of Δ u + K(|x|)f(u) = 0 in the exterior of the ball of radius $R > 0$ in RN with $ N > 2$ where f grows superlinearly at infinity and is singular at 0 with f ~ 1|u|q-1u where $0 < q < 1.$ We also assume K(r) ~ |r|- α for large r and establish the existence of two infinite families of solutions when N + q(N-2) < α < 2(N-1).