Geodesic
On Qualitative Properties of Differential-Algebraic Equations
Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 596-608

Voir la notice de l'article provenant de la source Math-Net.Ru

Linear systems of ordinary differential equations with identically degenerate coefficient matrix before the derivative of the unknown vector function are considered. The structure of general solutions and the notion of singular point of such systems are discussed. From the comparison of the properties of the “perturbed” and original problems, a sufficient criterion for the Lyapunov asymptotic stability of the zero solution is obtained.
Keywords: differential-algebraic equation, Lyapunov stability, Lyapunov asymptotic stability, regularizing operator, Euler difference scheme, Kronecker–Capelli condition. 
@article{MZM_2014_96_4_a10,
     author = {V. F. Chistyakov and Ta Duy Phuong},
     title = {On {Qualitative} {Properties} of {Differential-Algebraic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {596--608},
     publisher = {mathdoc},
     volume = {96},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a10/}
}
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V. F. Chistyakov; Ta Duy Phuong. On Qualitative Properties of Differential-Algebraic Equations. Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 596-608. http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a10/