  In the present work, we revisit the highly active research area of
inhomogeneously nonlinear defocusing media and consider the existence, spectral
stability and nonlinear dynamics of bright solitary waves in them. We use the
anti-continuum limit of vanishing coupling as the starting point of our
analysis, enabling in this way a systematic characterization of the branches of
solutions. Our stability findings and bifurcation characteristics reveal the
enhanced robustness and wider existence intervals of solutions with a broader
support, culminating in the "extended" solution in which all sites are excited.
Our eigenvalue predictions are corroborated by numerical linear stability
analysis. Finally, the dynamics also reveal a tendency of the solution profiles
to broaden, in line with the above findings. These results pave the way for
further explorations of such states in discrete systems, including in higher
dimensional settings.
