Back to the Keller-Osserman condition for boundary blow-up solutions
Résumé
This article is concerned with the existence, uniqueness and numerical approximation of boundary blow up solutions for elliptic PDE's as Δu=f(u) where f satisfies the so-called Keller-Osserman condition. We {\bleu characterize} existence of such solutions {\bleu for non-monotone f} . As an example, we construct an infinite family of boundary blow up solutions for the equation \bleuΔu=u2(1+cosu) on a ball. We {\bleu prove} uniqueness {\bleu (on balls) when} f is increasing and convex {\bleu in a} neighborhood of infinity and we discuss and perform some numerical computations to approximate such boundary blow-up solutions
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