Electronic Journal of Differential Equations, Vol. 2001(2001), No. 18, pp. 1-8. Title: Semilinear elliptic problems on unbounded subsets of the Heisenberg group Author: K. Tintarev (Uppsala Univ., Sweden) Abstract: In this paper we discuss the applications of an abstract version of concentration compactness to minimax problems. In particular, we prove the existence of solutions to semilinear elliptic problems on unbounded subsets of the Heisenberg group. Submitted January 17, 2001. Published March 20, 2001. Math Subject Classifications: 35J10, 35J20, 65K10. Key Words: Heisenberg group; elliptic equations; concentration compactness.