Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain

Let $\Omega$ be a bounded domain in $\mathbb{R}^{n}$ ($n\geq 2$) with a smooth boundary $\partial \Omega$. We discuss in this paper the existence and the asymptotic behavior of positive solutions of the following semilinear elliptic system $$\begin{aligned} -\Delta u&=a_{1}(x)u^{\alpha}v^{r}\quad\text{in}\;\Omega ,\;\;\,u|_{\partial\Omega}=0,\\ -\Delta v&=a_{2}(x)v^{\beta}u^{s}\quad\text{in}\;\Omega ,\;\;\,v|_{\partial\Omega }=0.\end{aligned}$$ Here $r,s\in \mathbb{R}$, $\alpha,\beta \lt 1$ such that $\gamma :=(1-\alpha)(1-\beta)-rs\gt 0$ and the functions $a_{i}$ ($i=1,2$) are nonnegative and satisfy some appropriate conditions with reference to Karamata regular variation theory

Positive solutions for systems of competitive fractional differential equations

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

Abstracts of 1st International Conference on Computational & Applied Physics

This book contains the abstracts of the papers presented at the International Conference on Computational & Applied Physics (ICCAP’2021) Organized by the Surfaces, Interfaces and Thin Films Laboratory (LASICOM), Department of Physics, Faculty of Science, University Saad Dahleb Blida 1, Algeria, held on 26–28 September 2021. The Conference had a variety of Plenary Lectures, Oral sessions, and E-Poster Presentations. Conference Title: 1st International Conference on Computational & Applied PhysicsConference Acronym: ICCAP’2021Conference Date: 26–28 September 2021Conference Location: Online (Virtual Conference)Conference Organizer: Surfaces, Interfaces, and Thin Films Laboratory (LASICOM), Department of Physics, Faculty of Science, University Saad Dahleb Blida 1, Algeria