A concentration-compactness principle at infinity and positive solutions of some quasilinear elliptic equations in unbounded domains

In this paper, we formulate a concentration-compactness principle at infinity which extends a result introduced by J. Chabrowski [Calc. Var. Partial Differential Equations 3 (1995) 493-512]. Then we consider some quasilinear elliptic equations in some classes of unbounded domains by solving their corresponding constrained minimization problems under certain conditions. We show the existence of positive solutions of those equations via the concentration-compactness principle at infinity, which extends some results in [Differential Integral Equations 6 (1993) 1281-1298].