Blow-up rates of large solutions for infinity Laplace equations

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

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