Abstract
Results on existence, multiplicity, stability, global continuation and limiting behaviour when ε↓0 of periodic solutions of
are derived for the case of a nonlinear functionf 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.
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Partially supported by NSF Grant MCS-8201768.
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Chow, S.N., Diekmann, O. & Mallet-Paret, J. Stability, multiplicity and global continuation of symmetric periodic solutions of a nonlinear Volterra integral equation. Japan J. Appl. Math. 2, 433–469 (1985). https://doi.org/10.1007/BF03167085
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DOI: https://doi.org/10.1007/BF03167085