Multibump solutions for quasilinear elliptic equations

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• 作者：Jia-Quan Liu^a ; Zhi-Qiang Wang^b ; ^{zhi-qiang.wang@usu.edu} ; Yu-Xia Guo^c
• 关键词：Multibump solutions ; Quasilinear elliptic equations ; Gluing method
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：1 May, 2012
• 卷：262
• 期：9
• 页码：4040-4102
• 文件大小：421 K

摘要

The current paper is concerned with constructing multibump type solutions for a class of quasilinear Schr枚dinger type equations including the Modified Nonlinear Schr枚dinger Equations. Our results extend the existence results on multibump type solutions in Coti Zelati and Rabinowitz (1992) 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.