Positive solutions for systems of competitive fractional differential equations
Year: 2016
Type: article
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.
Authors: Majda Chaieb, Abdelwaheb Dhifli, Malek Zribi
Institution: Tunis University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4392268947