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Browsing by Subject "Karamata regular variation theory"

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    Item type:Article, 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.