Abstract
Abstract Sufficient conditions are found for the global solvability of the weighted Cauchy problem where 𝑓 : 𝐶([𝑎, 𝑏]; 𝑅𝑛) → 𝐿𝑙𝑜𝑐(]𝑎, 𝑏]; 𝑅𝑛) is a singular Volterra operator, 𝑐0 ∈ 𝑅𝑛, : [𝑎, 𝑏] → [0, +∞[ is a function continuous and positive on ]𝑎, 𝑏], and ∥ · ∥ is the norm in 𝑅𝑛.
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