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On Some Elliptic Equation Involving the p(x)-Laplacian in \(\mathbb {R}^N\) with a Possibly Discontinuous Nonlinearities

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Abstract

In this paper, we prove some existence and uniqueness results for some elliptic quasilinear equation defined on the whole Euclidean space \( \mathbb {R}^N,\ N \ge 2\), involving the p(x)-Laplacian operator and whose nonlinearities can be discontinuous. Some new ideas and tools are used to reach our main results.

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Authors and Affiliations

  1. Department of Mathematics, High Institute of Applied Mathematics and Informatics of Kairouan, University of Kairouan, Avenue Assad Iben Fourat, 3100, Kairouan, Tunisia

    Sami Aouaoui

  2. Laboratory of Algebra, Number Theory and Nonlinear Analysis LR18ES15, Faculty of Sciences of Monastir, University of Monastir, Rue de l’environnement, 5019, Monastir, Tunisia

    Sami Aouaoui & Ala Eddine Bahrouni

  3. High School of Sciences and Technology of Hammam Sousse, University of Sousse, Rue Lamine ElAbbessi, 4011, Hammam Sousse, Tunisia

    Ala Eddine Bahrouni

Authors
  1. Sami Aouaoui
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  2. Ala Eddine Bahrouni
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Correspondence to Sami Aouaoui.

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Communicated by Maria Alessandra Ragusa.

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Aouaoui, S., Bahrouni, A.E. On Some Elliptic Equation Involving the p(x)-Laplacian in \(\mathbb {R}^N\) with a Possibly Discontinuous Nonlinearities. Bull. Malays. Math. Sci. Soc. 44, 1327–1344 (2021). https://doi.org/10.1007/s40840-020-01010-w

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  • DOI: https://doi.org/10.1007/s40840-020-01010-w

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