Multiple radial solutions for a semilinear dirichlet problem in a ball

We prove that a semilinear elliptic boundary value problem in a ball has 4j -1 radially symmetric solutions when the nonlinearity has a positive zero and the range of the derivative of the nonlinearity includes at least the first j eigenvalues. We make extensive use of the global bifurcation theorem, bifurcation from infinity, and bifurcation from simple eigenvalues.