Multibump solutions for quasilinear elliptic equations

The current paper is concerned with constructing multibump type solutions for a class of quasilinear Schrödinger type equations including the Modified Nonlinear Schrödinger 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.