Nonlocal Q-Laplacian Equation on the Heisenberg Group

In this paper, we are concerned with a new nonlocal Q-Laplacian equation on the Heisenberg group in the smooth bounded domain. The nonlinear term \(f(\xi ,u)\) $f(\xi ,u)$ has exponential growth behaving like \(\exp \bigg (\beta |t|^{\frac{Q}{Q-1}}\bigg )\) ${exp(\beta |t|}^{\frac{Q}{Q-1}})$ as \(|t|\rightarrow \infty \) $|t|\to \infty$ with some \(\beta >0\) $\beta >0$ . Existence of solutions are obtained by an application of the mountain pass theorem and Ekeland’s variational principle. Moreover, our results are new even on the Euclidean case.