Abstract:
In this paper, we study the existence of positive radial
solutions for a class of quasilinear systems of the form
$$
\begin{cases}
\Delta_{\phi_1}u=a_1(|x|)f_1(v),
\\
\Delta_{\phi_2}v=a_2(|x|)f_2(u),
\end{cases}
\quad x\in \mathbb{R}^N, \quad N\geqslant 3,
$$
where $\Delta_{\phi}w:=\operatorname{div}(\phi(|\nabla w|)\nabla w)$,
under appropriate conditions on the functions $\phi_1$, $\phi_2$,
the weights $a_1$, $a_2$ and the non-linearities $f_1$, $f_2$.
The conditions imposed for the existence of such solutions
are different from those in previous results.
Keywords:partial differential equations, cooperative systems, linear systems,
non-linear systems, methods of approximation.
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