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A Nontrivial Solution of a Quasilinear Elliptic Equation Via Dual Approach

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Abstract

In this article, we are concerned with the existence of solutions of a quasilinear elliptic equation in ℝN which includes the so-called modified nonlinear Schrödinger equation as a special case. Combining the dual approach and the nonsmooth critical point theory, we obtain the existence of a nontrivial solution.

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Acknowledgements

The authors would like to thank Dr. KeWu for helpful suggestions on the present article, as well as bringing their attention to [28] and [23].

Author information

Authors and Affiliations

  1. School of Preparatory Education, Yunnan Minzu University, Kunming, 650500, China

    Xianyong Yang

  2. School of Mathematics and Statistics, Central south University, Changsha, 410205, China

    Xianyong Yang

  3. Department of Mathematics, Yunnan University, Kunming, 650500, China

    Wei Zhang

  4. Department of Mathematics, Yunnan Normal University, Kunming, 650500, China

    Fukun Zhao

Authors
  1. Xianyong Yang
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  2. Wei Zhang
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  3. Fukun Zhao
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Corresponding author

Correspondence to Fukun Zhao.

Additional information

This work was supported partially by National Natural Science Foundation of China (11771385, 11661083) and the Youth Foundation of Yunnan Minzu University (2017QNo3).

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Yang, X., Zhang, W. & Zhao, F. A Nontrivial Solution of a Quasilinear Elliptic Equation Via Dual Approach. Acta Math Sci 39, 580–596 (2019). https://doi.org/10.1007/s10473-019-0220-8

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  • DOI: https://doi.org/10.1007/s10473-019-0220-8

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