INFINITELY MANY RADIAL SOLUTIONS FOR A p-LAPLACIAN PROBLEM WITH NEGATIVE WEIGHT AT THE ORIGIN

We prove the existence of infinitely many sign-changing radial solutions for a Dirichlet problem in a ball defined by the p-Laplacian operator perturbed by a nonlinearity of the form W(vertical bar x vertical bar)g(u), where the weight function W changes sign exactly once, W(0) < 0, W(1) > 0, and function g is p-superlinear at infinity. Standard phase plane analysis arguments do not apply here because the solutions to the corresponding initial value problem may blow up in the region where the weight function is negative. Our result extend those in [2], where W is assumed to be positive at 0 and negative at 1.