Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 107, pp. 1-12.

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

Author: Sami Aouaoui (Institut Superieur des Mathematiques, Kairouan, Tunisie)

Abstract:
 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.