  We study the semilinear wave equation with power type nonlinearity and small
initial data in Schwarzschild spacetime. If the nonlinear exponent $p$
satisfies $2\le p<1+\sqrt 2$, we establish the sharp upper bound of lifespan
estimate, while for the most delicate critical power $p=1+\sqrt2$, we show that
the lifespan satisfies
  \[
  T(\e)\le \exp\left(C\e^{-(2+\sqrt 2)}\right),
  \]
  the optimality of which remains to be proved. The key novelty is that the
compact support of the initial data can be close to the event horizon. By
combining the global existence result for $p>1+\sqrt 2$ obtained by Lindblad et
al.(Math. Ann. 2014), we then give a positive answer to the interesting
question posed by Dafermos and Rodnianski(J. Math. Pures Appl. 2005, the end of
the first paragraph in page $1151$): $p=1+\sqrt 2$ is exactly the critical
power of $p$ separating stability and blow-up.
