Geodesic
Solvability conditions in quadratures of two Volterra equations
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 90-98

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In terms of the coefficients of Volterra integral equations, sufficient conditions for their explicit solvability are derived. The conditions are obtained by the reduction of the initial equations to various versions of the Goursat problem for equations of second order. This makes it possible to use the known solutions to the Goursat problems in quadratures.
Mots-clés : Volterra equation, Goursat problem, solution in quadratures.
Keywords: Riemann function 
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     author = {I. M. Shakirova},
     title = {Solvability conditions in quadratures of two {Volterra} equations},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {90--98},
     publisher = {mathdoc},
     volume = {155},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a8/}
}
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I. M. Shakirova. Solvability conditions in quadratures of two Volterra equations. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 90-98. http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a8/