Boundary blow-up solutions to a class of degenerate elliptic equations

Let Omega be a bounded domain in R-N = R-N1 x R-N2 with N-1, N-2 = 1, and N(s) = N-1 + (1 + s)N-2 be the homogeneous dimension of R-N for s >= 0. In this paper, we prove the existence and uniqueness of boundary blow-up solutions to the following semilinear degenerate elliptic equation where denotes the Grushin distance from z to the boundary of Omega. Here Gs is the Grushin operator of the form It is worth noticing that our results do not require any assumption on the smoothness of the domain Omega, and when s = 0, we cover the previous results for the Laplace operator Delta.