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On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems. (English) Zbl 1042.35535
Let D be a bounded smooth domain in N . It is well known that large solutions of an equation such as Δu=u p , p>1 in D blow up at the boundary at a rate ϕ(δ) which depends only on p. (Here δ(x) denotes the distance of x to the boundary.) In this paper the authors consider a secondary effect in the asymptotic behaviour of solutions, namely, the behaviour of u/ϕ(δ)-1 as δ0. They derive estimates for this expression, which are valid for a large class of nonlinearities and extend a recent result of Lazer and McKenna.

MSC:
35J60Nonlinear elliptic equations
34C99Qualitative theory of solutions of ODE
35B40Asymptotic behavior of solutions of PDE