Multiplicity of large solutions for quasi-monotone pulse-type nonlinearities

Abstract

This paper discusses the Keller–Osserman condition from a dynamical perspective in order to obtain a rather astonishing multiplicity result of large solutions. It turns out that, for any given increasing positive function f(u) that satisfies the Keller–Osserman condition, destroying the monotonicity of f(u) on a compact set with arbitrarily small measure can originate an arbitrarily large number of explosive solutions. Moreover, some counterexamples to an important result of [6] are given.