On a class of singular elliptic problems with first order terms

Abstract

We give a complete classification over the range of parameters for existence or nonexistence both of global and of local solutions to a class of semilinear elliptic problems with a first order term and singular coefficients, as well as of solutions to the related Dirichlet problem in bounded domains containing the origin. We also investigate symmetry properties of ground state solutions, proving that symmetry breaking occurs in a suitable range of parameters.