Periodic Solutions of an Integrodifferential Equation Modelling Resonant Sloshing

This paper considers the problem of finding solutions of which have period 2 and mean 0. The equation models periodicgravity waves on the surface of a shallow rectangular tank whichis oscillating longitudinally near the primary resonance frequency.The singular integral memory term is well behaved, and the Lyapunov-Schmidtprocedure produces bifurcation equations to which the analysisof Hale & Rodrigues on the damped Duffing equation is directlyapplicable. The multiplicity of all small solutions of the equationis found as (µ₁µ₂µ₃) varies in a full neighbourhoodof 0 in R³.