TY - JOUR

T1 - Singular perturbed integro-differential Volterra equation and Drazin's inverse singular matrices

AU - Goltser, Ya

AU - Domoshnitsky, A.

N1 - Funding Information:
This research was supported by The Israel Science Foundation (grant No. 828/07).

PY - 2009/12/15

Y1 - 2009/12/15

N2 - We consider integro-differential system of the form A (μ) frac(d x, d t) = B (μ) x + G (t, μ, x) + ∫0t K (t, s, μ) φ (x (s, μ)) d s, where the coefficients A (μ), B (μ), G (t, μ, x) and K (t, s, μ) continuously depend on a vector parameter μ, and the matrix A (μ) is singular at μ = 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.

AB - We consider integro-differential system of the form A (μ) frac(d x, d t) = B (μ) x + G (t, μ, x) + ∫0t K (t, s, μ) φ (x (s, μ)) d s, where the coefficients A (μ), B (μ), G (t, μ, x) and K (t, s, μ) continuously depend on a vector parameter μ, and the matrix A (μ) is singular at μ = 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.

UR - http://www.scopus.com/inward/record.url?scp=72149130516&partnerID=8YFLogxK

U2 - 10.1016/j.na.2009.02.048

DO - 10.1016/j.na.2009.02.048

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AN - SCOPUS:72149130516

SN - 0362-546X

VL - 71

SP - e1765-e1770

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 12

ER -