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On Singular Quasilinear Elliptic Equations in \(\mathbb {R}^N\)

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Abstract

In this paper we investigate the existence of solutions for two classes of singular quasilinear elliptic problems in \(\mathbb {R}^N.\) For the first class of problems, we use a change of variable with global minimization argument and prove the existence and uniqueness of solution. For the second class of problems, we use a change of variable with local minimization argument and an application of a version of the mountain pass theorem combined with a truncation argument to obtain two solutions.

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Funding

The first author is partially supported by CNPq/Brazil Proc. No 306709-2022-8 and by FAP-DF/Brazil. The second author is partially supported by CNPq, Capes and FAP-DF/Brazil. The third author is partially supported by CAPES/Brazil.

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Authors and Affiliations

  1. Faculdade de Matemática, Universidade Federal do Pará, Belém, PA, CEP: 66.075-110, Brazil

    Gelson C. G. dos Santos

  2. Departamento de Matemática, Universidade de Brasília, Brasília, DF, CEP: 70910-900, Brazil

    Giovany M. Figueiredo

  3. Faculdade de Ciências Naturais, Matemática e Estatística, Universidade Rovuma, CEP: 544, Nampula, Mozambique

    Sábado Saide Muhassua

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  1. Gelson C. G. dos Santos
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  2. Giovany M. Figueiredo
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  3. Sábado Saide Muhassua
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Correspondence to Gelson C. G. dos Santos.

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Santos, G.C.G.d., Figueiredo, G.M. & Muhassua, S.S. On Singular Quasilinear Elliptic Equations in \(\mathbb {R}^N\). J Geom Anal 33, 293 (2023). https://doi.org/10.1007/s12220-023-01356-0

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  • DOI: https://doi.org/10.1007/s12220-023-01356-0

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