Existence of solutions and boundary asymptotic behavior of p(r)p(r)-Laplacian equation multi-point boundary value problems

This paper investigates the problem {−Δp(r)u+ρ(r)f(r,u)=0,r∈(0,R),u(0)=∑i=1mαiu(ηi)+e0,u(r)→+∞(as r→R−), where −Δp(r)u=−(|u′|p(r)−2u′)′−Δp(r)u=−(|u′|p(r)−2u′)′ is called the p(r)p(r)-Laplacian, ρ(r)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.