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.
Fulltext:
PDF file (608 kB)
