existence, nonexistence and asymptotic behavior of boundary blow-up solutions to p(x)-laplacian problems with singular coefficient

{−δ_p(x)u + ρ(x)f (x, u) = 0 in ,

u(x) → +∞ as d(x, ∂) → 0,

where −δ_p(x)u = −div(|∇u|^p(x)−2 ∇u) is called the p(x)-laplacian, and ρ(x) is a singular coefficient. the existence and nonexistence of boundary blow-up solutions is discussed, and the asymptotic behavior of boundary blow-up solutions is given. in particular, we do not assume radial symmetric conditions, and the pointwise different exact blow-up rate of solutions has been discussed.