  We propose analytical lower and upper estimates on the excitation threshold
for breathers (in the form of spatially localized and time periodic solutions)
in DNLS lattices with power nonlinearity. The estimation depending explicitly
on the lattice parameters, is derived by a combination of a comparison argument
on appropriate lower bounds depending on the frequency of each solution with a
simple and justified heuristic argument. The numerical studies verify that the
analytical estimates can be of particular usefulness, as a simple analytical
detection of the activation energy for breathers in DNLS lattices.
