Browsing by Author "Zermani, Samia"

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Access status: Open Access ,
Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain
(2016) Chaieb, Majda; Dhifli, Abdelwaheb; Zermani, Samia
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.
Access status: Open Access ,
Existence and boundary behavior of positive solutions for a Sturm-Liouville problem
(2016) Masmoudi, Syrine; Zermani, Samia
In this paper, we discuss existence, uniqueness and boundary behavior of a positive solution to the following nonlinear Sturm-Liouville problem $\begin{aligned}&\frac{1}{A}(Au^{\prime })^{\prime }+a(t)u^{\sigma}=0\;\;\text{in}\;(0,1),\\ &\lim\limits_{t\to 0}Au^{\prime}(t)=0,\quad u(1)=0,\end{aligned}$ where $\sigma \lt 1$, $A$ is a positive differentiable function on $(0,1)$ and $a$ is a positive measurable function in $(0,1)$ satisfying some appropriate assumptions related to the Karamata class. Our main result is obtained by means of fixed point methods combined with Karamata regular variation theory.