On the qualitative behavior of solutions for a quasilinear \(\Delta _p\) equation in the Heisenberg group

In this article, by using the the direct method in the calculus of variations, the existence of weak solutions to a quasilinear class of \(\Delta _p\) ${\mathrm{\Delta }}_p$ equations on the Heisenberg group \({\mathbb {H}}^n\) ${\mathbb{H}}^n$ is investigated. The equation incorporates a critical Sobolev exponent, a gradient term representing a drift effect, and zero boundary condition.