Periodic Solution for Almost Linear Volterra Integro-dynamic Matrix Sylvester System on Measure Chains - Chintamaneni, Harisha; Bhogapurapu, Venkata Appa Rao; Ayyalappagari, Sreenivasulu (Discontinuity, Nonlinearity, and Complexity, 2026)
The primary aim of this paper is to identify periodic solutions within an almost linear Volterra Integro-dynamic matrix Sylvester system operating on measure chains. Initially, we undertake a transformation of the Volterra Integro-dynamic matrix Sylvester system into the Kronecker Product Volterra Integro-dynamic System on measure chains through vectorization operations. Subsequent to this transformation, we proceed to establish the existence of periodic solutions for the Kronecker Product Volterra Integro-dynamic system on measure chains, by using Banach fixed point theorem. Importantly, our investigation extends to encompass periodic measure chains operating under both continuous and discrete conditions.