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

Recommended by Ivan Kiguradze

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.