Singular perturbed integro-differential Volterra equation and Drazin’s inverse singular matrices Original Research Article

We consider integro-differential system of the form View the MathML sourceA(μ)dxdt=B(μ)x+G(t,μ,x)+∫0tK(t,s,μ)φ(x(s,μ))ds, Turn MathJax on where the coefficients A(μ),B(μ),G(t,μ,x)A(μ),B(μ),G(t,μ,x) and K(t,s,μ)K(t,s,μ) continuously depend on a vector parameter μμ, and the matrix A(μ)A(μ) is singular at μ=0μ=0. For analysis of this system, a method based on its reduction to a countable singular system of ordinary differential equations is proposed. The finite sections method and an application of Drazin’s inverse matrices to the integration of linear singular systems are used.