On some quasilinear equation with critical exponential growth at infinity and a singular behavior at the origin

  • Sami Aouaoui


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.


Multiplicity Singularity Exponential growth Trudinger–Moser inequality Concentration-compactness 

Mathematical Subject Classification

35A25 35D30 35J20 35J62 35J75 



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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© Orthogonal Publishing and Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut Supérieur des Mathématiques Appliquées et de l’Informatique de KairouanKairouanTunisia

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