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Anisotropic (p, q)-equations with superlinear reaction

Ricerche di Matematica (2022)Cite this article

Abstract

In this paper, we consider a Dirichlet problem driven by the anisotropic (p, q)-Laplacian and a superlinear reaction which need not satisfy the Ambrosetti–Robinowitz condition. By using variational tools together with truncation and comparison techniques and critical groups, we show the existence of at least five nontrivial smooth solutions, all with sign information: two positive, two negative and a nodal (sign-changing).

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Acknowledgements

This project has received funding from the NNSF of China Grant Nos. 12001478 and 12101143, the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 823731 CONMECH, National Science Center of Poland under Preludium Project No. 2017/25/N/ST1/00611, and the Startup Project of Doctor Scientific Research of Yulin Normal University No. G2020ZK07. It is also supported by Natural Science Foundation of Guangxi Grants Nos. 2021GXNSFFA196004, 2020GXNSFBA297137 and GKAD21220144, the Ministry of Science and Higher Education of Republic of Poland under Grant No. 440328/PnH2/2019, and the National Science Centre of Poland under Project No. 2021/41/B/ST1/01636.

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Authors and Affiliations

  1. School of Science, Guangxi University of Science and Technology, Liuzhou, 545006, Guangxi, People’s Republic of China

    Yunru Bai

  2. Department of Mathematics, National Technical University, Zograrou Campus, Athens, 15780, Greece

    Nikolaos S. Papageorgiou

  3. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, People’s Republic of China

    Shengda Zeng

  4. Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu, People’s Republic of China

    Shengda Zeng

  5. Jagiellonian University in Krakow, aculty of Mathematics and Computer Science, ul. Lojasiewicza 6, 30348, Kraków, Poland

    Shengda Zeng

Authors
  1. Yunru Bai
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  2. Nikolaos S. Papageorgiou
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  3. Shengda Zeng
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Correspondence to Shengda Zeng.

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Bai, Y., Papageorgiou, N.S. & Zeng, S. Anisotropic (p, q)-equations with superlinear reaction. Ricerche mat (2022). https://doi.org/10.1007/s11587-022-00702-8

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  • DOI: https://doi.org/10.1007/s11587-022-00702-8

Keywords

  • Anisotropic regularity
  • Extremal constant sign solutions
  • Nodal solution
  • Critical point theory
  • Critical group

Mathematics Subject Classification

  • 35J60
  • 35J20