Blow-up rates of large solutions for infinity Laplace equations

摘要

In this paper, by constructing suitable comparison functions, we mainly give the boundary behavior of solutions to boundary blow-up elliptic problems ▵∞u=b(x)f(u),x∈Ω,u|∂Ω=+∞, where Ω is a bounded domain with smooth boundary in RN, the operator △∞ is the ∞-Laplacian, b∈Cα(Ω¯) which is positive in Ω and may be vanishing on the boundary and rapidly varying near the boundary and the nonlinear term f is a Γ-varying function at infinity, whose variation at infinity is not regular.