Multiple solutions for semilinear cone elliptic equations without Ambrosetti–Rabinowitz condition

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Abstract

In this paper we establish the existence of multiple solutions for a class of semilinear cone degenerate elliptic Dirichlet boundary value problems involving subcritical nonlinearity (cone Sobolev exponent) without the Ambrosetti–Rabinowitz condition. The paper uses singular analysis to control the linear part to provide appropriate functional setting that a variation of the Moutain Pass argument can be applied.

Keywords

Cone-degenerate operators Cone Laplace–Beltrami Cerami sequences Fountain theorem Subcritical growth 

Mathematics Subject Classification

35J20 35J10 35J70 35A15 35D30 

Notes

Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions to improve the quality of the paper. This work is supported by the Hanoi University of Science and Technology under Project No. T2016–PC–204.

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Copyright information

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Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationCau GiayViet Nam
  2. 2.School of Applied Mathematics and InformaticsHanoi University of Science and TechnologyHai Ba TrungViet Nam

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