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 th...

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Bibliographic Details
Published in:Journal of functional analysis 2012-05, Vol.262 (9), p.4040-4102
Main Authors: Liu, Jia-Quan, Wang, Zhi-Qiang, Guo, Yu-Xia
Format: Article
Language:English
Subjects:
Gluing method
Multibump solutions
Quasilinear elliptic equations
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Summary: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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2012.02.009