Positive weak solutions of a generalized supercritical Neumann problem

The aim of this paper is to show that a supercritical Neumann problem has at least one positive radial solution via recent variational principle and defining an energy functional with a hidden symmetry associated with the problem. Also, we study the problem in the setting of the Heisenberg group $${\mathbb {H}}^n$$ , which is a special case of locally compact groups.