Electron. J. Diff. Equ., Vol. 2015 (2015), No. 197, pp. 1-15.

Nonlinear elliptic problems involving the n-Laplacian with maximal growth

Abderrahim El Attar, Said El Manouni, Omar Sidki

Abstract:
In this article, we study the limit case of some elliptic problems involving nonlinearities having the maximal growth with Dirichlet boundary conditions. We apply a result by Ricceri [12] to prove the existence of multiple nontrivial solutions using Trudinger-Moser estimates.

Submitted July 6, 2015. Published July 30, 2015.
Math Subject Classifications: 35J35, 35J60, 35J66.
Key Words: Limit case; maximal growth; Trudinger-Moser's inequality; Ricceri's principle.

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Abderrahim El Attar
University of Fez, FST
Department of Mathematics
Fez, Morocco
email: abderrahimelattar@hotmail.com
Said El Manouni
Al Imam Mohammad Ibn Saud Islamic University (IMSIU)
Faculty of Sciences, Department of Mathematics
P.O. Box 90950
Riyadh 11623, Saudi Arabia
email: samanouni@imamu.edu.sa
  Omar Sidki
University of Fez, FST
Department of Mathematics
Fez, Morocco
email: osidki@hotmail.com

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