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On positive solutions for a class of quasilinear elliptic equations

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Abstract

This paper studies the existence, nonexistence and uniqueness of positive solutions for a class of quasilinear equations. We also analyze the behavior of these solutions with respect to two parameters \(\kappa \) and \(\lambda \) that appear in the equation. The proof of our main results relies on bifurcation techniques, the sub- and supersolution method and a construction of an appropriate large solution.

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Acknowledgements

Research partially supported by CAPES and CNPq Grants 308735/2016-1 and 307770/2015-0. The authors thank to the referee for her/his comments and suggestions which improve notably this work.

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  1. Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, PB, 58051-900, Brazil

    Willian Cintra, Everaldo Medeiros & Uberlandio Severo

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  1. Willian Cintra
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  2. Everaldo Medeiros
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  3. Uberlandio Severo
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Correspondence to Willian Cintra.

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Cintra, W., Medeiros, E. & Severo, U. On positive solutions for a class of quasilinear elliptic equations. Z. Angew. Math. Phys. 70, 79 (2019). https://doi.org/10.1007/s00033-019-1121-3

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