Advances in Difference Equations
Volume 2010 (2010), Article ID 262854, 17 pages
Research Article

Positive and Dead-Core Solutions of Two-Point Singular Boundary Value Problems with ϕ-Laplacian

Department of Mathematical Analysis, Faculty of Science, Palacký University, Tř. 17. listopadu 12, 771 46 Olomouc, Czech Republic

Received 18 December 2009; Accepted 15 March 2010

Academic Editor: Leonid Berezansky

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.


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, β0, γ0, f is singular at u=0, and f may be singular at u'=0.