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Ground states for quasilinear Schrödinger equations with critical growth

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Abstract

For a class of quasilinear Schrödinger equations with critical exponent we establish the existence of both one-sign and nodal ground states of soliton type solutions by the Nehari method. The method is to analyze the behavior of solutions for subcritical problems from our earlier work (Liu et al. Commun Partial Differ Equ 29:879–901, 2004) and to pass limit as the exponent approaches to the critical exponent.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan Normal University, Kunming, 650092, People’s Republic of China

    Xiangqing Liu

  2. LMAM, School of Mathematical Science, Peking University, Beijing, 100871, People’s Republic of China

    Jiaquan Liu

  3. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, People’s Republic of China

    Zhi-Qiang Wang

  4. Department of Mathematics and Statistics, Utah State University, Logan, UT, 84322, USA

    Zhi-Qiang Wang

Authors
  1. Xiangqing Liu
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  2. Jiaquan Liu
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  3. Zhi-Qiang Wang
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Correspondence to Zhi-Qiang Wang.

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Communicated by P. Rabinowitz.

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Liu, X., Liu, J. & Wang, ZQ. Ground states for quasilinear Schrödinger equations with critical growth. Calc. Var. 46, 641–669 (2013). https://doi.org/10.1007/s00526-012-0497-0

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  • DOI: https://doi.org/10.1007/s00526-012-0497-0

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