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

  • S. Chen
  • X. Tang
Article
  • 4 Downloads

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.

Key words and phrases

logarithmic nonlinearity ground state solution sign-changing solution 

Mathematics Subject Classification

35J20 35J65 

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Notes

Acknowledgement

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

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCentral South UniversityChangsha, HunanP. R. China

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