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

This paper investigates the problem {-Delta(p(x))u + rho(x)f(x, u) = 0 in Omega, u(x) -> +infinity as d(x, partial derivative Omega) -> 0, where -Delta(p(x))u = -div(vertical bar del u vertical bar(p(x)-2)del u) is called the p(x)-Laplacian, and rho(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. Published by Elsevier Ltd