Solutions to a perturbed critical semilinear equation concerning the $N$-Laplacian in $\mathbb {R}^{N}$

Tonkes, Elliot. "Solutions to a perturbed critical semilinear equation concerning the $N$-Laplacian in $\mathbb {R}^{N}$." Commentationes Mathematicae Universitatis Carolinae 40.4 (1999): 679-699. <http://eudml.org/doc/248432>.

@article{Tonkes1999,
abstract = {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 $u \in W_0^\{1,N\}(\mathbb \{R\}^\{N\})$, $\Omega $ is a bounded smooth domain in $\mathbb \{R\}^\{N\}$, $N \ge 2$, $e(x,u)$ is a critical nonlinearity in the sense of the Trudinger-Moser inequality and $h(x) \in (W_0^\{1,N\})^*$ is a small perturbation.},
author = {Tonkes, Elliot},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {variational methods; elliptic equations; critical growth; variational methods; elliptic equations; critical growth},
language = {eng},
number = {4},
pages = {679-699},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Solutions to a perturbed critical semilinear equation concerning the $N$-Laplacian in $\mathbb \{R\}^\{N\}$},
url = {http://eudml.org/doc/248432},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Tonkes, Elliot
TI - Solutions to a perturbed critical semilinear equation concerning the $N$-Laplacian in $\mathbb {R}^{N}$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 4
SP - 679
EP - 699
AB - 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 $u \in W_0^{1,N}(\mathbb {R}^{N})$, $\Omega $ is a bounded smooth domain in $\mathbb {R}^{N}$, $N \ge 2$, $e(x,u)$ is a critical nonlinearity in the sense of the Trudinger-Moser inequality and $h(x) \in (W_0^{1,N})^*$ is a small perturbation.
LA - eng
KW - variational methods; elliptic equations; critical growth; variational methods; elliptic equations; critical growth
UR - http://eudml.org/doc/248432
ER -

References

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Citations in EuDML Documents

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Robert Černý, Generalized $n$ -Laplacian: semilinear Neumann problem with the critical growth

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