Section 4.3 of "Introduction to Algorithms, 3rd Edition By Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein" uses the following recurrence as an example to illustrate the substitution method.
$T(n) = 2T(\lfloor{n/2}\rfloor)+n \tag{4.19}$
That section says
Let us assume, for the sake of argument, that T(1) = 1 is the sole boundary condition of the recurrence.
In reality, does there exist any other boundary condition of the recurrence (4.19)?