Boundary Value Problems
Volume 2007 (2007), Article ID 18961, 16 pages
doi:10.1155/2007/18961
Research Article

Dead Core Problems for Singular Equations with φ-Laplacian

Ravi P. Agarwal,1 Donal O'Regan,2 and Svatoslav Staněk3

1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901-6975, Florida, USA
2Department of Mathematics, National University of Ireland, Galway, Ireland
3Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, Olomouc 779 00, Czech Republic

Received 27 May 2007; Accepted 6 September 2007

Academic Editor: Ivan Kiguradze

Copyright © 2007 Ravi P. Agarwal et al. 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′))′+f(t,u′)=λg(t,u,u′), u′(0)=0, βu′(T)+αu(T)=A. Here λ is a positive parameter, β≥0, α, A>0, f may be singular at t=0 and g is singular at u=0.