Geodesic
Abstract degenerate non-scalar Volterra equation
Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 1, pp. 104-112.

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In this paper, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations by investigating abstract degenerate non-scalar Volterra equations. We consider the generation of $(A,k,B)$-regularized $C$-pseudoresolvent families in Banach spaces, as well as their analytical properties and hyperbolic perturbation results.
Keywords: abstract degenerate differential equation, non-scalar Volterra equation, degenerate $(A,k)$-regularized $C$-pseudoresolvent family, degenerate fractional resolvent family, well-posedness. 
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M. Kostić. Abstract degenerate non-scalar Volterra equation. Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 1, pp. 104-112. http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_1_a10/

[1] J. Prüss, Evolutionary Integral Equations and Applications, Birkhäuser-Verlag Publ., Basel, 1993 | MR | Zbl

[2] M. Kostić, “Generalized well-posedness of hyperbolic Volterra equations of non-scalar type”, Annals of the Academy of Romanian Scientists. Series on Mathematics and its Applications, 6 (2014), 21–49 | MR | Zbl

[3] M. Jung, “Duality theory for solutions to Volterra integral equation”, Journal of Mathematical Analysis and Applications, 230 (1999), 112–134 | DOI | MR | Zbl

[4] A. Karczewska, “Stochastic Volterra equations of nonscalar type in Hilbert space”, Transactions XXV International Seminar on Stability Problems for Stochastic Models, eds. C. D'Apice et al., University of Salerno, 2005, 78–83

[5] M. Kostić, Generalized Semigroups and Cosine Functions, Mathematical Institute SANU Publ., Belgrade, 2011 | MR | Zbl

[6] M. Kostić, Abstract Volterra Integro-Differential Equations, Taylor and Francis Group/CRC Press/Science Publ., Boca Raton, New York, 2015 | MR

[7] R. W. Carroll, R. E. Showalter, Singular and Degenerate Cauchy Problems, Academic Press Publ., New York, 1976 | MR

[8] G. V. Demidenko, S. V. Uspenskii, Partial Differential Equations And Systems Not Solvable With Respect To The Highest-Order Derivative, Pure and Applied Mathematics, 256, CRC Press Publ., New York, 2003 | MR

[9] A. Favini, A. Yagi, Degenerate Differential Equations in Banach Spaces, Chapman and Hall/CRC Pure and Applied Mathematics Publ., New York, 1998 | MR

[10] I. V. Melnikova, A. I. Filinkov, Abstract Cauchy Problems: Three Approaches, Chapman and Hall/CRC Publ., Boca Raton, 2001 | MR | Zbl

[11] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, Inverse and Ill-Posed Problems, 42, VSP Publ., Utrecht–Boston, 2003 | MR

[12] W. Arendt, C. J. K. Batty, M. Hieber, F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Birkhäuser Verlag, 2001 | MR