Electron. J. Diff. Equ., Vol. 2014 (2014), No. 107, pp. 1-12.

Existence of multiple solutions to elliptic problems of Kirchhoff type with critical exponential growth

Sami Aouaoui

In this article, we study elliptic problems of Kirchhoff type in dimension $ N \geq 2$, whose nonlinear term has a critical exponential growth. Using variational tools, we establish the existence of at least two nontrivial and nonnegative solutions.

Submitted December 10, 2013. Published April 15, 2014.
Math Subject Classifications: 35D30, 35J20, 35J61, 58E05.
Key Words: Trudinger-Moser inequality; exponential growth; Kirchhoff equation; critical point; energy functional; Ekeland's lemma; Mountain Pass Theorem.

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Sami Aouaoui
Institut Supérieur des Mathématiques Appliquées et de l'Informatique de Kairouan
Avenue Assad Iben Fourat, 3100 Kairouan, Tunisie
email: aouaouisami@yahoo.fr
Phone +216 77 226 575, Fax +216 77 226 575

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