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Sbornik: Mathematics, 2008, Volume 199, Issue 4, Pages 557–578
DOI: https://doi.org/10.1070/SM2008v199n04ABEH003933
(Mi sm3697)
 

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
References:
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
Russian version:
Matematicheskii Sbornik, 2008, Volume 199, Number 4, Pages 83–106
DOI: https://doi.org/10.4213/sm3697
Bibliographic databases:
UDC: 517.956.2
MSC: Primary 35J55; Secondary 35J65
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2008v199n04ABEH003933
  • https://www.mathnet.ru/eng/sm/v199/i4/p83
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:474
    Russian version PDF:214
    English version PDF:7
    References:45
    First page:10
     
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