Geodesic
Existence of multiple solutions to elliptic problems of Kirchhoff type with critical exponential growth
Electronic journal of differential equations, Tome 2014 (2014)
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.
Classification : 35D30, 35J20, 35J61, 58E05
Keywords: Trudinger-Moser inequality, exponential growth, Kirchhoff equation, critical point, energy functional, Ekeland's lemma, mountain pass theorem 
@article{EJDE_2014__2014__a60,
     author = {Aouaoui,  Sami},
     title = {Existence of multiple solutions to elliptic problems of {Kirchhoff} type with critical exponential growth},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1328.35023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a60/}
}
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%A Aouaoui,  Sami
%T Existence of multiple solutions to elliptic problems of Kirchhoff type with critical exponential growth
%J Electronic journal of differential equations
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Aouaoui,  Sami. Existence of multiple solutions to elliptic problems of Kirchhoff type with critical exponential growth. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a60/