  In this paper we use the full Maxwell equations for light propagation in
order to analyze plasmonic resonances for nanoparticles. We mathematically
define the notion of plasmonic resonance and analyze its shift and broadening
with respect to changes in size, shape, and arrangement of the nanoparticles,
using the layer potential techniques associated with the full Maxwell
equations. We present an effective medium theory for resonant plasmonic systems
and derive a condition on the volume fraction under which the Maxwell-Garnett
theory is valid at plasmonic resonances.
