Geodesic
On the Well-Posedness of the Cauchy Problem for Quasilinear Differential Equations of Neutral Type
Contemporary Mathematics. Fundamental Directions, Optimal control, Tome 19 (2006), pp. 179-197

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The paper proves the theorems on the continuous dependence of solutions when perturbations of the initial moment, the initial vector, the initial functions, the matrix coefficients, am the nonlinear summand in the right-hand side are small in the Euclidean and integral topologies, respectively. 
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     author = {T. A. Tadumadze and N. Z. Gorgodze and I. V. Ramishvili},
     title = {On the {Well-Posedness} of the {Cauchy} {Problem} for {Quasilinear} {Differential} {Equations} of {Neutral} {Type}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {179--197},
     publisher = {mathdoc},
     volume = {19},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2006_19_a7/}
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T. A. Tadumadze; N. Z. Gorgodze; I. V. Ramishvili. On the Well-Posedness of the Cauchy Problem for Quasilinear Differential Equations of Neutral Type. Contemporary Mathematics. Fundamental Directions, Optimal control, Tome 19 (2006), pp. 179-197. http://geodesic.mathdoc.fr/item/CMFD_2006_19_a7/