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Ground state sign-changing solutions for elliptic equations with logarithmic nonlinearity

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Abstract

We study elliptic equations with logarithmic nonlinearity. With the help of the constraint variational method, quantitative deformation lemma and some new energy inequalities, we establish the existence of ground state solutions and ground state sign-changing solutions with precisely two nodal domains. Our result complements the existing ones on Schrödinger problems since the logarithmic nonlinearity is sign-changing, and satisfies neither the monotonicity condition nor Ambrosetti–Rabinowitz condition.

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Acknowledgement

The authors thank the anonymous referees for their valuable suggestions and comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, P. R. China

    S. Chen & X. Tang

Authors
  1. S. Chen
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  2. X. Tang
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Correspondence to S. Chen.

Additional information

This work is partially supported by the National Natural Science Foundation of China (11571370, 11701487, 11626202) and Hunan Provincial Natural Science Foundation of China (2016JJ6137)

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Chen, S., Tang, X. Ground state sign-changing solutions for elliptic equations with logarithmic nonlinearity. Acta Math. Hungar. 157, 27–38 (2019). https://doi.org/10.1007/s10474-018-0891-y

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  • DOI: https://doi.org/10.1007/s10474-018-0891-y

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