Geodesic
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/}
}
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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/