Soliton solutions for quasilinear Schrodinger equations:: The critical exponential case

Quasilinear elliptic equations in 1182 of second order with critical exponential growth are considered. By using a change of variable, the quasilinear equations are reduced to semilinear equations, whose respective associated functionals are well defined in H 1(12) and satisfy the geometric hypotheses of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle [P.L. Lions, The concentration compactness principle in the calculus of variations. The locally compact case. Part I and II, Ann. Inst. H. Poincare Anal. Non. Lineaire 1 (1984) 109-145, 223-283] combined with test functions connected with optimal Trudinger-Moser inequality. (c) 2006 Elsevier Ltd. All rights reserved.