Abstract
The main purpose of this paper is to investigate the existence and the asymptotic behavior of positive continuous solutions of the following nonlinear coupled system: \(\begin{cases} -\dfrac{1}{A}(Au')'= a(x)u^pv^r\quad\text{on}\ \ (0,1), \\[10 pt] -\dfrac{1}{B}(Bv')'=b(x)v^q u^s\quad\text{on}\ \ (0,1), \\[10 pt] u(0)=u(1)=v(0)=v(1)=0, \end{cases}\) where \(p,q \in (-1,1)\) and \(r,s \in \mathbb{R}\) are such that \( (1- |p |)(1-| q |)-|rs | >0\) . The functions \(A\) and \(B\) are positive and differentiable on \((0,1) \) , and the positive weight functions \(a\) and \(b\) may be singular at the boundary and satisfy some appropriate assumptions related to the Karamata class.
