Multibump solutions for quasilinear elliptic equations |
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Authors: | Jia-Quan Liu Zhi-Qiang Wang Yu-Xia Guo |
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Affiliation: | 1. LMAM, School of Mathematical Science, Peking University, Beijing, 100871, PR China;2. Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA;3. Department of Mathematics, Tsinghua University, Beijing, 100084, PR China |
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Abstract: | 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. |
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