Authors’ abstract: The blow-up of solutions of the Cauchy problem,
is studied. Let be the set of functions on which change sign times. It is shown that for
any solution with blows up in finite time if , whereas a global solution with exists if . It is also shown that if decays more slowly than as , then the solution blows up in finite time regardless of the number of sign changes.
Part I, see Math. Ann. 307, No. 4, 663-675 (1997; Zbl 0872.35046).