### Global attractor of coupled difference equations and applications to Lotka-Volterra systems.

Pao, C.V. (2005)

Advances in Difference Equations [electronic only]

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Pao, C.V. (2005)

Advances in Difference Equations [electronic only]

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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 $$-{\Delta}_{N}u\equiv -{div\left(\right|\nabla u|}^{N-2}\nabla u)=e(x,u)+h\left(x\right)\phantom{\rule{4.0pt}{0ex}}\text{in}\phantom{\rule{4.0pt}{0ex}}\Omega $$ where $u\in {W}_{0}^{1,N}\left({\mathbb{R}}^{N}\right)$, $\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 $h\left(x\right)\in {\left({W}_{0}^{1,N}\right)}^{*}$ is a small perturbation.