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 -