Positive solutions for one-dimensional singular $p$-Laplacian boundary value problems
Volume 105 / 2012
Annales Polonici Mathematici 105 (2012), 125-144
MSC: Primary 35J70; Secondary 35J25.
DOI: 10.4064/ap105-2-2
Abstract
We consider the existence of positive solutions of the equation $$ {1\over \lambda (t)}(\lambda (t)\varphi _p(x'(t)))'+ \mu f(t,x(t),x'(t))=0, $$ where $\varphi _p(s)=|s|^{p-2}s, p>1$, subject to some singular Sturm–Liouville boundary conditions. Using the Krasnosel'skiĭ fixed point theorem for operators on cones, we prove the existence of positive solutions under some structure conditions.
