On some elliptic equation in the whole euclidean space $  \mathbb{R}^2  $ with nonlinearities having new exponential growth condition

Sami Aouaoui; Rahma Jlel

doi:10.3934/cpaa.2020211

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2020, Volume 19, Issue 10: 4771-4796. Doi: 10.3934/cpaa.2020211

This issue Previous Article Uniqueness of positive radial solutions of the Brezis-Nirenberg problem on thin annular domains on

$ {\mathbb S}^n $

and symmetry breaking bifurcations Next Article Global bifurcation for the Hénon problem

On some elliptic equation in the whole euclidean space $ \mathbb{R}^2 $ with nonlinearities having new exponential growth condition

Sami Aouaoui^1, , and
Rahma Jlel^2,

1.
Institut Supérieur des Mathématiques Appliquées et de, l'Informatique de Kairouan, Avenue Assad Iben Fourat, Kairouan, 3100, Tunisie
2.
Faculté des Sciences de Monastir, Avenue de l'environnement 5019 Monastir, Tunisie

^* Corresponding author
^* Corresponding author

Received: May 2019

Revised: May 2020

Published online: October 2020

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Abstract

In this paper, we study some elliptic equation defined in $ \mathbb{R}^2 $ and involving a nonlinearity with new exponential growth condition including the doubly exponential growth at infinity. For that aim, we start by extending some new Trudinger-Moser type inequalities defined on the unit ball of different classes of weighted Sobolev spaces established by B. Ruf and M. Calanchi to the whole space $ \mathbb{R}^2. $

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Mathematics Subject Classification: Primary: 35A15, 35D30, 35J20; Secondary: 35J61.

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References

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