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Soliton solutions for a quasilinear Schrödinger equation via Morse theory

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Abstract

In this paper, Morse theory is used to show the existence of nontrivial weak solutions to a class of quasilinear Schrödinger equation of the form

$-{\Delta }_{p} u-\frac {p}{2^{p-1}}u{\Delta }_{p}(u^{2})=f(x,u)$

in a bounded smooth domain \({\Omega }\subset \mathbb {R}^{N}\) with Dirichlet boundary condition.

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Acknowledgements

The authors would like to thank the referee for a careful reading of an earlier version of the paper and valuable suggestions. This research is supported by the National Natural Science Foundation of China (NSFC 11471147) and Fundamental Research Funds for the Central Universities (lzujbky-2014-25).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    DUCHAO LIU & PEIHAO ZHAO

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  1. DUCHAO LIU
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  2. PEIHAO ZHAO
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Correspondence to DUCHAO LIU.

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Communicating Editor: Parameswaran Sankaran

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LIU, D., ZHAO, P. Soliton solutions for a quasilinear Schrödinger equation via Morse theory. Proc Math Sci 125, 307–321 (2015). https://doi.org/10.1007/s12044-015-0240-9

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  • DOI: https://doi.org/10.1007/s12044-015-0240-9

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