Geodesic
Nonexplicit evolution Volterra integral equation of the first kind with nonlinear integral delay
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 119 (2009) no. 2, pp. 38-44 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove a theorem of existence, uniqueness and stability of solution of the implicit evolution Volterra integral equation with respect to the initial value condition on the given finite segment. Here we use the method of successive approximation in combination with the method of compressing mapping.
Mots-clés : implicit Volterra integral equation
Keywords: existence and uniqueness of solutions. 
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     title = {Nonexplicit evolution {Volterra} integral equation of the first kind with nonlinear integral delay},
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T. K. Yuldashev. Nonexplicit evolution Volterra integral equation of the first kind with nonlinear integral delay. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 119 (2009) no. 2, pp. 38-44. http://geodesic.mathdoc.fr/item/VSGTU_2009_119_2_a4/

[1] Yuldashev T. K., Artykova Zh. A., “Integralnoe uravnenie Volterra pervogo roda s nelineinoi pravoi chastyu”, Skladni sistemi i protsesi, 2005, no. 1–2, 3–5

[2] Yuldashev T. K., Artykova Zh. A., “Integralnye uravneniya Volterra pervogo roda s nelineinoi pravoi chastyu i slozhnym otkloneniem”, Geometriya v Odesse—2005. Differents. geometriya i ee prilozheniya, Tez. mezhdunarodn. seminara (23–29 maya 2005 g.), Odessa, 2005, 112–113

[3] Yuldashev T. K., Artykova J. A., “Volterra functional integral equation of the first kind with nonlinear right-hand side and variable limits of integration”, Ukr. mat. zhurn., 58:9 (2006), 1285–1288 | MR | Zbl

[4] Yuldashev T. K., Artykova Zh. A., “Evolyutsionnoe integralnoe uravnenie Volterra s integralnymi otkloneniyami”, Vestn. UlGTU, 2006, no. 3, 18–20 | Zbl

[5] Yuldashev T. K., “On a summary equation with weak nonlinear right-hand side”, Advanced stud. in contemp. math., 15:1 (2007), 95–98 | MR | Zbl