Analysis of classes of singular steady state reaction diffusion equations

We study positive radial solutions to classes of steady state reaction diffusion problems on the exterior of a ball with both Dirichlet and nonlinear boundary conditions. We study both Laplacian as well as p-Laplacian problems with reaction terms that are p-sublinear at infinity. We consider both positone and semipositone reaction terms and establish existence, multiplicity and uniqueness results. Our existence and multiplicity results are achieved by a method of sub-supersolutions and uniqueness results via a combination of maximum principles, comparison principles, energy arguments and a-priori estimates. Our results significantly enhance the literature on p-sublinear positone and semipositone problems. Finally, we provide exact bifurcation curves for several one-dimensional problems. In the autonomous case, we extend and analyze a quadrature method, and in the nonautonomous case, we employ shooting methods. We use numerical solvers in Mathematica to generate the bifurcation curves