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A priori estimates, existence and non-existence for quasilinear cooperative elliptic systems
Sbornik. Mathematics, Tome 199 (2008) no. 4, pp. 557-578 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $m>1$ be a real number and let $\Omega\subset\mathbb R^n$, $n\geqslant2$, be a connected smooth domain. Consider the system of quasi-linear elliptic differential equations \begin{align*} \operatorname{div}(|\nabla u|^{m-2}\nabla u)+f(u,v)&=0\quad\text{in } \Omega, \\ \operatorname{div}(|\nabla v|^{m-2}\nabla v)+g(u,v)&=0\quad\text{in } \Omega, \end{align*} where $u\geqslant0$, $v\geqslant0$, $f$ and $g$ are real functions. Relations between the Liouville non-existence and a priori estimates and existence on bounded domains are studied. Under appropriate conditions, a variety of results on a priori estimates, existence and non-existence of positive solutions have been established. Bibliography: 11 titles. 
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     title = {A priori estimates, existence and non-existence for quasilinear cooperative elliptic systems},
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H. Zou. A priori estimates, existence and non-existence for quasilinear cooperative elliptic systems. Sbornik. Mathematics, Tome 199 (2008) no. 4, pp. 557-578. http://geodesic.mathdoc.fr/item/SM_2008_199_4_a4/

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