(ii) For fixed Ψ(u 0 ) and δ,
P(u 0 , u 1 ) → |I δ | = β δ − α δ ,
is strictly increasing, and we have the limit values lim P(u0,u1)→∞
α δ = 0 = lim P(u0,u1)→∞ β δ − 1 2 Φ(u 0 , u 1 ) , lim P(u0,u1)→∞ ν * = ∞, lim P(u0,u1)→∞ λ * = r − 2 − δ/ √ c r − δ/ √ c .
Corollary 1. Assume that hypotheses of Theorem 3.1 are met. For every number K > 0, we can choose initial **data** with P(u 0 , u 1 ) large enough, so that K ∈ I δ , and then the corresponding solution with E 0 = K exists only up to a finite time.