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

Abstract

<abstract><p>A variational principle is applied to examine a Muckenhoupt weighted $ p(\cdot) $-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.</p></abstract>