We investigate the Brézis–Nirenberg problem (Comm. Pure Appl. Math., 36: 437-477, 1983) for the Kohn Laplacian on Heisenberg group within a partially symmetric, smooth, and bounded domain \(\Omega \) that satisfies certain geometric conditions. By employing a subcritical approximation to the critical method developed by Devillanova and Solimini (Adv. Differential Equations, 7: 1257-1280, 2002), we establish uniform bound estimates for partially symmetric balanced sequences when the homogeneous dimension \(Q \ge 8\) (see Theorem 1.1 below). Additionally, we obtain the existence of infinitely many partially symmetric sign-changing solutions to the Kohn Laplacian equation with critical nonlinearity (see Theorem 1.2 of this paper). Furthermore, we present some regularity results for weak solutions of the Kohn Laplacian equation (see Proposition 2.3 of this paper).
