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On an Anisotropic Eigenvalue Problem

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Abstract

We consider a nonlinear eigenvalue problem driven by the anisotropic (p, q)-Laplacian. Using variational tools and truncation and comparison techniques, we show the existence of a continuous spectrum (a bifurcation-type theorem). We also show the existence of a minimal positive solution and determine the properties of the minimal solution map.

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Data Availability Statement

Data availability is not applicable to this manuscript as no new data were generated or analyzed during the current study.

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Authors and Affiliations

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

    Zhenhai Liu

  2. Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, College of Mathematics and Physics, Guangxi Minzu University, Nanning, 530006, Guangxi, People’s Republic of China

    Zhenhai Liu

  3. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece

    Nikolaos S. Papageorgiou

Authors
  1. Zhenhai Liu
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  2. Nikolaos S. Papageorgiou
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Correspondence to Zhenhai Liu.

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The work was supported by NSF of Guangxi Grant No. 2023GXNSFAA026085, Guangxi Science and Technology Department Specific Research Project of Guangxi for Research Bases and Talents Grant No. AD23023001, NNSF of China Grant No. 12071413, the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 823731 CONMECH.

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Liu, Z., Papageorgiou, N.S. On an Anisotropic Eigenvalue Problem. Results Math 78, 178 (2023). https://doi.org/10.1007/s00025-023-01954-y

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