Stability, multiplicity and global continuation of symmetric periodic solutions of a nonlinear Volterra integral equation

Results on existence, multiplicity, stability, global continuation and limiting behaviour when ε↓0 of periodic solutions of {Mathematical expression} are derived for the case of a nonlinear function f having certain monotonicity and symmetry properties. The proofs are based on the following two observations: (i) the right-hand side of (E) defines an operator which maps a cone of two-periodic functions with symmetry and positivity properties into itself; and (ii) slowly oscillating solutions of the linear variational equation correspond to dominant Floquet multipliers.