Multiple Sign-Changing Solutions for a Class of Schrödinger Equations with Saturable Nonlinearity

Abstract

In this paper, we construct sign-changing radial solutions for a class of Schrödinger equations with saturable nonlinearity which arises from several models in mathematical physics. More precisely, for any given nonnegative integer k, by using a minimization argument, we first obtain a sign-changing minimizer with k nodes of a constrained minimization problem, and show, by a deformation lemma and Miranda’s theorem, that the minimizer is the desired solution.

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Correspondence to Zhongyuan Liu.

Additional information

The author is supported by National Natural Science Foundation of China (11971147), China Postdoctoral Science Foundation (2019M662475) and Henan Postdoctoral Research Grant (201902026).

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Cite this article

Liu, Z. Multiple Sign-Changing Solutions for a Class of Schrödinger Equations with Saturable Nonlinearity. Acta Math Sci 41, 493–504 (2021). https://doi.org/10.1007/s10473-021-0213-2

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Key words

  • Sign-changing solutions
  • saturable nonlinearity
  • Nehari manifold
  • variational methods

2010 MR Subject Classification

  • 35J61
  • 35J66
  • 35Q55
  • 35Q60