{'fraction_non_alphanumeric': 0.015734265734265736, 'fraction_numerical': 0.0, 'mean_word_length': 4.96875, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The limit periodic solutions of the Volterra-type integro-differential equations in the critical case of a single zero root

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.