Multibump solutions for quasilinear elliptic equations

The current paper is concerned with constructing multibump type solutions for a class of quasilinear Schrodinger type equations including the Modified Nonlinear Schrodinger Equations. Our results extend the existence results on multibump type solutions in Coti Zelati and Rabinowitz (1992) [17] to the quasilinear case. Our work provides a theoretic framework for dealing with quasilinear problems, which lack both smoothness and compactness, by using more refined variational techniques such as gluing techniques. Morse theory, Lyapunov-Schmidt reduction, etc. (C) 2012 Elsevier Inc. All rights reserved.