Electron. J. Diff. Equ., Vol. 2016 (2016), No. 133, pp. 1-13.

Positive solutions for systems of competitive fractional differential equations

Majda Chaieb, Abdelwaheb Dhifli, Malek Zribi

Abstract:
Using potential theory arguments, we study the existence and boundary behavior of positive solutions in the space of weighted continuous functions, for the fractional differential system
$$\displaylines{ D^{\alpha }u(x)+p(x)u^{a_1}(x)v^{b_1}(x) =0\quad \text{in }(0,1),\quad \lim_{x\to 0^{+}}x^{1-\alpha }u(x)=\lambda >0, \cr D^{\beta }v(x)+q(x)v^{a_2}(x)u^{b_2}(x) = 0\quad \text{in }(0,1),\quad \lim_{x\to 0^{+}}x^{1-\beta }v(x)=\mu >0, }$$
where $\alpha,\beta \in (0,1)$, $a_i>1$, $b_i\geq 0$ for $i\in \{1,2\}$ and $p,q$ are positive continuous functions on $(0,1)$ satisfying a suitable condition relying on fractional potential properties.

Submitted February 27, 2016 Published June 7, 2016.
Math Subject Classifications: 26A33, 31B25, 34A12, 34B18.
Key Words: Fractional differential system; positive solution; potential theory; Schauder fixed point theorem.

Show me the PDF file (256 KB), TEX file for this article.

Majda Chaieb
Département de Mathématiques
Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: majda.chaieb@gmail.com
Abdelwaheb Dhifli
Département de Mathématiques
Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: dhifli_waheb@yahoo.fr
Malek Zribi
Département de Mathématiques
Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: malek.zribi@insat.rnu.tn

Return to the EJDE web page