Existence of positive radial solutions for a problem involving the weighted Heisenberg p(⋅)-Laplacian operator

A variational principle is applied to examine a Muckenhoupt weighted p(⋅)-Laplacian equation on the Heisenberg groups. The existence of at least one positive radial solution to the problem under the Dirichlet boundary condition belongs to the first order Heisenberg-Sobolev spaces is proved.