TY  - JOUR
ID  - Masmoudi2016
LB  - Masmoudi2016
AU  - Masmoudi, Syrine
AU  - Zermani, Samia
TI  - Existence and boundary behavior of positive solutions for a Sturm-Liouville problem
ST  - Existence and boundary behavior of positive solutions for a Sturm-Liouville problem
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 5
SP  - 613
EP  - 629
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.5.613
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.5.613
AB  - 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.
KW  - nonlinear Sturm-Liouville problem
KW  - Green's function
KW  - positive solutions
KW  - Karamata regular variation theory
SN  - 1232-9274
ER  -