On critical exponential Kirchhoff systems on the Heisenberg group

Abstract

In this paper, existence of solutions is established for critical exponential Kirchhoff systems on the Heisenberg group by using the variational method. The novelty of our paper is that not only the nonlinear term has critical exponential growth, but also that Kirchhoff function covers the degenerate case. Moreover, our result is new even for the Euclidean case.

Anisotropic Moser–Trudinger-Type Inequality with Logarithmic Weight

“…These important geometric inequalities play a key role in geometry analysis, calculus of variations, and PDEs; we refer to [9][10][11][12][13][14] and references therein. And recently, the authors of [15] studied a system of Kirchhoff type driven by the Q-Laplacian in the Heisenberg group H n . They obtained the existence of solutions via variational methods based on a new Moser-Trudinger-type inequality for the Heisenberg group H n .…”