We consider the problem (Formula presented.) where (Formula presented.), n>2, λ is a positive parameter, (Formula presented.) belongs to a class of continuous functions which satisfy certain decay assumptions, and (Formula presented.) belongs to a class of continuous functions which are superlinear at ∞ with (Formula presented.). Recently, several authors have studied positive radial solutions to this problem assuming that the weight function is radial. We allow non-radial weights and study the existence and non-existence of positive solutions. We prove the existence of a positive solution for small values of λ using variational methods. A non-existence result is established for large values of λ. © 2021 Informa UK Limited, trading as Taylor & Francis Group.