  This work analyzes the effects of cubic nonlinearities on certain resonant
scattering anomalies associated with the dissolution of an embedded eigenvalue
of a linear scattering system. These sharp peak-dip anomalies in the frequency
domain are often called Fano resonances. We study a simple model that
incorporates the essential features of this kind of resonance. It features a
linear scatterer attached to a transmission line with a point-mass defect and
coupled to a nonlinear oscillator. We prove two power laws in the small
coupling <gamma> \to 0 and small nonlinearity <mu> \to 0 regime. The asymptotic
relation <mu> ~ C<gamma>^4 characterizes the emergence of a small frequency
interval of triple harmonic solutions near the resonant frequency of the
oscillator. As the nonlinearity grows or the coupling diminishes, this interval
widens and, at the relation <mu> ~ C<gamma>^2, merges with another evolving
frequency interval of triple harmonic solutions that extends to infinity. Our
model allows rigorous computation of stability in the small <mu> and <gamma>
limit. In the regime of triple harmonic solutions, those with largest and
smallest response of the oscillator are linearly stable and the solution with
intermediate response is unstable.
