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

Dead Core Problems for Singular Equations with φ-Laplacian

Ravi P. Agarwal1 , Donal O'Regan2 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

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.