A note on derivative dependent singular boundary value problems arising in physiology

Abstract

In this note we establish existence of solutions of singular boundary value problem $-(p(x)y^{\prime }(x){)}^{\prime }=q(x)f(x,y,p{y}^{\prime })$ for $0<x\le b$ and $y^{\prime }(0)=0$, ${\alpha }_{1}y(b)+{\beta }_{1}p(b)y^{\prime }(b)={\gamma }_1$ with $p(0)=0$ and $q(x)$ is integrable. Regions of multiple solutions have also been determined.

arXiv comment12 pages