Abstract
In this paper, we prove the existence of at least two solutions to some quasilinear equation involving the N-Laplacian operator in the whole space \( \mathbb {R}^N,\ N \ge 2. \) The nonlinearity consists of two terms: one has a critical exponential growth at infinity governed by the Trudinger–Moser inequality, and the other one presents a singularity at the origin. A combination of perturbation arguments together with variational tools is employed to obtain our multiplicity result.
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The author is very grateful to the anonymous referees for their careful reading of the manuscript and their insightful and constructive remarks and comments that helped to clarify the content and improve the presentation of the results in this paper.
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To the memory of my dear friend Professor Mohamed Benrhouma.
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Aouaoui, S. On some quasilinear equation with critical exponential growth at infinity and a singular behavior at the origin. J Elliptic Parabol Equ 4, 27–50 (2018). https://doi.org/10.1007/s41808-018-0012-7
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DOI: https://doi.org/10.1007/s41808-018-0012-7