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Quasilinear equations involving indefinite nonlinearities and exponential critical growth in \({\mathbb {R}}^N\)

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Abstract

In this work, we establish the existence of nonzero solutions for a class of quasilinear elliptic equations involving indefinite nonlinearities with exponential critical growth of Trudinger–Moser type. Our proofs rely on variational arguments in a Orlicz–Sobolev space with a version of the Trudinger–Moser inequality.

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Acknowledgements

Part of this work was done while the second author was visiting the Instituto de Ciências Matemáticas e de Computação—ICMC—USP. He would like to thank professor Sérgio H. M. Soares for his hospitality. We would like to thank the referee for carefully reading the paper and giving many useful comments and important suggestions which substantially helped in improving the quality of the paper.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Estadual da Paraíba, Campina Grande, PB, CEP 58429-500, Brasil

    Luciana R. de Freitas

  2. UAMAT, Universidade Federal de Campina Grande, Campina Grande, PB, CEP 58109-970, Brasil

    Jefferson Abrantes Santos

  3. Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, PB, CEP 58051-900, Brasil

    Uberlandio B. Severo

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  1. Luciana R. de Freitas
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  2. Jefferson Abrantes Santos
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  3. Uberlandio B. Severo
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Correspondence to Jefferson Abrantes Santos.

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Jefferson A. Santos: Research partially supported by CNPq-Brazil Grant Casadinho/Procad 552.464/2011-2. Uberlandio B. Severo: Research partially supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and CNPq Grant 308735/2016-1.

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de Freitas, L.R., Abrantes Santos, J. & Severo, U.B. Quasilinear equations involving indefinite nonlinearities and exponential critical growth in \({\mathbb {R}}^N\). Annali di Matematica 200, 315–335 (2021). https://doi.org/10.1007/s10231-020-00997-0

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  • DOI: https://doi.org/10.1007/s10231-020-00997-0

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