Geodesic
Solutions to a perturbed critical semilinear equation concerning the $N$-Laplacian in $\Bbb R^{N}$
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 679-699.

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The aim of this paper is to study the existence of variational solutions to a nonhomogeneous elliptic equation involving the $N$-Laplacian $$ - \Delta_N u \equiv - \operatorname{div} (|\nabla u|^{N-2} \nabla u) = e(x,u) + h(x) \text{ in } \Omega $$ where $u \in W_0^{1,N}(\Bbb R^{N})$, $\Omega$ is a bounded smooth domain in $\Bbb R^{N}$, $N \geq 2$, $e(x,u)$ is a critical nonlinearity in the sense of the Trudinger-Moser inequality and $h(x) \in (W_0^{1,N})^*$ is a small perturbation.
Classification : 35B20, 35B33, 35B34, 35J20, 35J60, 35J65
Keywords: variational methods; elliptic equations; critical growth 
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     author = {Tonkes, Elliot},
     title = {Solutions to a perturbed critical semilinear equation concerning the $N${-Laplacian} in $\Bbb R^{N}$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {679--699},
     publisher = {mathdoc},
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     zbl = {1064.35511},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_1999__40_4_a6/}
}
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Tonkes, Elliot. Solutions to a perturbed critical semilinear equation concerning the $N$-Laplacian in $\Bbb R^{N}$. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 679-699. http://geodesic.mathdoc.fr/item/CMUC_1999__40_4_a6/