Copyright © 2010 Svatoslav Staněk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper discusses the existence of positive solutions, dead-core solutions, and pseudo-dead-core solutions of the singular problem (ϕ(u′))′=λf(t,u,u′), u(0)-αu′(0)=A, u(T)+βu′(0)+γu′(T)=A. Here λ is a positive parameter, α>0, A>0, β≥0, γ≥0, f is singular at u=0, and f may be singular at u'=0.