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Anisotropic (pq)-equations with superlinear reaction

Abstract

In this paper, we consider a Dirichlet problem driven by the anisotropic (pq)-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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Correspondence to Shengda Zeng.

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Bai, Y., Papageorgiou, N.S. & Zeng, S. Anisotropic (pq)-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