Existence theorems for a~class of systems involving two quasilinear operators
Izvestiya. Mathematics , Tome 83 (2019) no. 1, pp. 49-64
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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.
@article{IM2_2019_83_1_a2,
author = {D.-P. Covei},
title = {Existence theorems for a~class of systems involving two quasilinear operators},
journal = {Izvestiya. Mathematics },
pages = {49--64},
publisher = {mathdoc},
volume = {83},
number = {1},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_1_a2/}
}
D.-P. Covei. Existence theorems for a~class of systems involving two quasilinear operators. Izvestiya. Mathematics , Tome 83 (2019) no. 1, pp. 49-64. http://geodesic.mathdoc.fr/item/IM2_2019_83_1_a2/