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This article is cited in 3 scientific papers (total in 3 papers)
A priori estimates, existence and non-existence for quasilinear cooperative elliptic systems
H. Zou University of Alabama at Birmingham
Abstract:
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.
Received: 25.09.2006 and 17.07.2007
Citation:
H. Zou, “A priori estimates, existence and non-existence for quasilinear cooperative elliptic systems”, Mat. Sb., 199:4 (2008), 83–106; Sb. Math., 199:4 (2008), 557–578
Linking options:
https://www.mathnet.ru/eng/sm3697https://doi.org/10.1070/SM2008v199n04ABEH003933 https://www.mathnet.ru/eng/sm/v199/i4/p83
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Abstract page: | 474 | Russian version PDF: | 214 | English version PDF: | 7 | References: | 45 | First page: | 10 |
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