Constructions of harmonic maps between Hadamard manifolds

1.3. ADDENDUM 41
Theorem 1.2.11. There exists a global, positive and strictly monotone increasing solution
r = r(t) satisfying
lim r(t) =∞.
t→∞
Proof. Fix t 0 > 0 arbitrarily. Then, it follows from Theorem 1.2.8 and Theorem 1.2.10
that there exist sequences of positive numbers {T i } ∞ i=1, {l j } ∞ j=1 and sequences of solutions
{r i } ∞ i=1, {r j } ∞ j=1 to the equation (1.1.1) with the boundary condition (1.1.2) so that
0