Multiple positive solutions to elliptic boundary blow-up problems

We prove the existence of multiple positive radial solutions to a sign-indefinite elliptic boundary blow-up problem where the nonlinearity is a function superlinear at zero and at infinity and is multiplied by a sign changing weight function. In particular, we show how the number of solutions is affected by the nodal behavior of the weight function. The proof is based on a careful shooting-type argument for the equivalent singular ODE problem. As a further application of this technique, the existence of multiple positive radial homoclinic solutions is also considered