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Multiple Nontrivial Solutions for Superlinear Double Phase Problems Via Morse Theory

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Abstract

The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools together with suitable truncation and minimax techniques with Morse theory, the authors prove the existence of one and three nontrivial weak solutions, respectively.

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Acknowledgement

The authors would like to thank the anonymous reviewers for their careful reading and valuable comments.

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Authors and Affiliations

  1. College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, China

    Bin Ge, Beilei Zhang & Wenshuo Yuan

Authors
  1. Bin Ge
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  2. Beilei Zhang
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  3. Wenshuo Yuan
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Corresponding author

Correspondence to Bin Ge.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11201095), the Fundamental Research Funds for the Central Universities (No. 3072022TS2402), the Postdoctoral research startup foundation of Heilongjiang (No. LBH-Q14044) and the Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province (No. LC201502).

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Cite this article

Ge, B., Zhang, B. & Yuan, W. Multiple Nontrivial Solutions for Superlinear Double Phase Problems Via Morse Theory. Chin. Ann. Math. Ser. B 44, 49–66 (2023). https://doi.org/10.1007/s11401-023-0004-2

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  • DOI: https://doi.org/10.1007/s11401-023-0004-2

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