Analysis and numerical simulation of positive and dead-core solutions of singular two-point boundary value problems

We investigate the solvability of the Dirichlet boundary value problem where λ is a nonnegative parameter. We discuss the existence of multiple positive solutions and show that for certain values of λ, there also exist solutions that vanish on a subinterval [ρ,1−ρ] (0,1), the so-called dead-core solutions. In order to illustrate the theoretical findings, we present computational results for , computed using the collocation method implemented in bvpsuite, a new version of the standard MATLAB code sbvp1.0.