Large solutions with a power nonlinearity given by a variable exponent for pp-Laplacian equations

In this paper we establish the existence, uniqueness and blow-up rate near the boundary of boundary blow-up solutions to pp-Laplacian elliptic equations with a power nonlinearity given by a variable exponent −Δpu=b(x)uq(x)−Δpu=b(x)uq(x), where Δpu=div(|∇u|p−2∇u) with p>1p>1. Here we combine the localization method originated by López-Gómez (2003) with some previous radially symmetric results to get the asymptotic behavior near the boundary.