Geodesic
Existence of bounded positive solutions of a nonlinear differential system
Electronic journal of differential equations, Tome 2012 (2012)
In this article, we study the existence and nonexistence of solutions for the system

$\displaylines{ \frac{1}{A}(Au')'=pu^{\alpha }v^{s}\quad \hbox{on }(0,\infty ), \cr \frac{1}{B}(Bu')'=qu^{r}v^{\beta }\quad \hbox{on }(0,\infty ), \cr Au'(0)=0,\quad u(\infty )=a>0, \cr Bv'(0)=0,\quad v(\infty )=b>0, }$

where $\alpha ,\beta \geq 1, s,r\geq 0$, p,q are two nonnegative functions on $(0,\infty )$ and A, B satisfy appropriate conditions. Using potential theory tools, we show the existence of a positive continuous solution. This allows us to prove the existence of entire positive radial solutions for some elliptic systems.
Classification : 35J56, 31B10, 34B16, 34B27
Keywords: nonlinear equation, Green's function, asymptotic behavior, singular operator, positive solution 
@article{EJDE_2012__2012__a92,
     author = {Gontara,  Sabrine},
     title = {Existence of bounded positive solutions of a nonlinear differential system},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1244.34031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a92/}
}
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Gontara,  Sabrine. Existence of bounded positive solutions of a nonlinear differential system. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a92/