This paper investigates the problem {(- Δp (r) u + ρ(r) f (r, u) = 0, r ∈(0, R),;u (0) = underover(∑, i = 1, m) αi u (ηi) + e0, u (r) &rarr + ∞(as r &rarr R-),) where - Δp (r) u = - (| u′ |p (r) - 2 u′)′ is called the p (r)-Laplacian, ρ(r) is a singular coefficient. The existence and nonexistence of solutions are discussed, and the exact boundary blow-up rate of solutions is given. ©2009 Elsevier Ltd.
