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Existence of Solutions to Nonlinear Schrödinger Equations Involving N-Laplacian and Potentials Vanishing at Infinity

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Abstract

We study the existence of solutions for the following class of nonlinear Schrödinger equations −Δnu + V(x)u = K(x)f(u)in ℝN where V and K are bounded and decaying potentials and the nonlinearity f(s) has exponential critical growth. The approaches used here are based on a version of the Trudinger-Moser inequality and a minimax theorem.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212013, P. R. China

    Mao Chun Zhu, Jun Wang & Xiao Yong Qian

Authors
  1. Mao Chun Zhu
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  2. Jun Wang
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  3. Xiao Yong Qian
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Corresponding authors

Correspondence to Mao Chun Zhu, Jun Wang or Xiao Yong Qian.

Additional information

The research of the first author was partially supported by Natural Science Foundation of China (Grant Nos. 11601190 and 11661006), Natural Science Foundation of Jiangsu Province (Grant No. BK20160483) and Jiangsu University Foundation Grant (Grant No. 16JDG043)

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Zhu, M.C., Wang, J. & Qian, X.Y. Existence of Solutions to Nonlinear Schrödinger Equations Involving N-Laplacian and Potentials Vanishing at Infinity. Acta. Math. Sin.-English Ser. 36, 1151–1170 (2020). https://doi.org/10.1007/s10114-020-0020-z

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  • DOI: https://doi.org/10.1007/s10114-020-0020-z

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