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Parametric Singular Problems with an Indefinite Perturbation

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Abstract

We consider a parametric Dirichlet problem driven by a nonhomogenous differential operator. In the parametric reaction we have the competing effects of a singular term and of a superlinear perturbation which is sign-changing. Using variational tools together with truncation and comparison techniques we show that for all small values of the parameter the problem has at least two smooth solutions.

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Acknowledgements

The authors thank the two anonymous reviewers for their corrections and remarks. The third author was supported by the grant “Nonlinear Differential Systems in Applied Sciences” of the Romanian Ministry of Research, Innovation and Digitization within PNRR-III-C9-2022-I8 (Grant No.22).

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Authors and Affiliations

  1. Faculty of Applied Mathematics, AGH University of Krakow, al. A. Mickiewicza 30, 30-059, Kraków, Poland

    Krzysztof Bień & Witold Majdak

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

    Nikolaos S. Papageorgiou

  3. Department of Mathematics, University of Craiova, 200585, Craiova, Romania

    Nikolaos S. Papageorgiou

Authors
  1. Krzysztof Bień
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  2. Witold Majdak
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  3. Nikolaos S. Papageorgiou
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Correspondence to Witold Majdak.

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Bień, K., Majdak, W. & Papageorgiou, N.S. Parametric Singular Problems with an Indefinite Perturbation. J Geom Anal 34, 103 (2024). https://doi.org/10.1007/s12220-024-01549-1

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