The limit periodic solutions of the Volterra-type integro-differential equations in the critical case of a single zero root

摘要

The equations with non-linear terms in a form of power series with respect to variable and functionals are investigated. The equations depend on a small limit periodic perturbation. In the critical case of a single zero root, the existence of the limit periodic solutions family of the integro-differential equation is proved in form holomorphic functions with respect to a small parameter and arbitrary initial data of the non-critical variables.