Positive and nodal solutions for a parametric quasilinear $Q$-sub-Laplacian problem with critical exponential growth on the Heisenberg group

In this article, we investigate the following modified quasilinear equation with parameter driven by the $Q$-subLaplacian: \begin{align*} \begin{cases} -Δ_Q u - Δ_Q\bigl(|u|^{2α}\bigr)\,|u|^{2α-2} u = λf(ξ,u) & \text{in } Ω, \\[2mm] u = 0 & \text{on } \partialΩ, \end{cases} \end{align*} where $Δ