Electron. J. Diff. Equ., Vol. 2012 (2012), No. 58, pp. 1-9.

Existence of bounded positive solutions of a nonlinear differential system

Sabrine Gontara

Abstract:
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.

Submitted January 20, 2012. Published April 10, 2012.
Math Subject Classifications: 35J56, 31B10, 34B16, 34B27.
Key Words: Nonlinear equation; Green's function; asymptotic behavior; singular operator; positive solution.

Show me the PDF file (208 KB), TEX file, and other files for this article.

Sabrine Gontara
Dépatement de mathématiques
Faculté des sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: sabrine-28@hotmail.fr

Return to the EJDE web page