Back to the Keller-Osserman condition for boundary blow-up solutions

This article is concerned with the existence, uniqueness and numerical approximation of boundary blow up solutions for elliptic PDE’s ∆u = f(u), where f satisfies the so-called Keller-Osserman condition. We characterize existence of such solutions for non-monotone f. As an example, we construct an infinite family of boundary blow up solutions for the equation ∆u = u2(1 + cosu) on a ball. We prove uniqueness (on balls) when f is increasing and convex in a neighborhood of infinity and we discuss and perform some numerical computations to approximate such boundary blow-up solutions. 2000 AMS Mathematics Subject Classification. 35J60. Key words. Elliptic equations, boundary blow-up, Keller-Osserman conditio