Xác định hệ số và điều kiện biên trong bài toán giá trị biên cho phương trình integro-phương trình vi phân với hạt suy biến

N. D. Bang, V. F. Chistyakov, and E. V. Chistyakova, “On some properties of degenerate system of linear integro-differential equations. I,” Izv. Irkutsk. Univ. 11, 13–27 (2015). Ya. V. Bykov, On Some Problems of the Theory of Integro-Differential Equations (Frunze, 1957) [in Russian]. M. M. Vajnberg, “Integro-differential equations,” Itogi Nauki, Ser.Mat. Anal. Teor. Veroyatn. Regulir. 1962, 5–37 (1964). V. V. Vasil’ev, “To the problem of solution of the Cauchy problem for a class of linear integro-differential equations,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 8–24 (1961). T. I. Vigranenko, “On a class of linear integro-differential equations,” Zap. Leningr. Gorn. Inst. 33, 176–186 (1956). V. V. Vlasov and R. Perez Ortiz, “Spectral analysis of integro-differential equations in viscoelasticity and thermal physics,” Math. Notes 98, 689–693 (2015). L. E. Krivoshein, “On a method of solving the some integro-differential equations,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 168–172 (1960). Yu. K. Lando, “Boundary value problem for Volterra linear integro-differential equations in the case of disjoint boundary value conditions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 56–65 (1961). G. A. Shishkin, “Justification a method of solving Fredholm integro-differential equations with functional delay,” in Correct Boundary Problems for Non-Classical Mathematical Physics Equations (Inst. Mat. Sib. Otdel. AN SSSR, Novosibirsk, 1980), pp. 172–178 [in Russian]. M. V. Phalaleev, “Integro-differential equations with Fredholm operator on the highest derivative in Banach spaces and their applications,” Izv. Irkutsk. Univ., Ser. Mat. 5 (2), 90–102 (2012). A. M. Denisov, Introduction to the Theory of Inverse Problem (Mosk. Gos. Univ., Moscow, 1994) [in Russian] A. B. Kostin, “The inverse problem of recovering the source in a parabolic equation under a condition of nonlocal observation,” Sbornik: Math. 204, 1391–1434 (2013). M. M. Lavrent’ev and L. Ya. Savel’ev, Linear Operators and Ill-Posed Problems (Nauka, Moscow, 1991) [in Russian]. A. I. Prilepko and A. B. Kostin, “On certain inverse problems for parabolic equations with final and integral observation,” Sbornik: Math. 75, 473–490 (1992). A. I. Prilepko and I. V. Tikhonov, “Restoring nonhomogeneous term in an abstract evolution equation,” Izv. Akad. Nauk, Mat. 58, 167–188 (1994). A. I. Prilepko and D. S. Tkachenko, “Properties of solutions of a parabolic equation and the uniqueness of the solution of the inverse source problem with integral over determination,” Comp. Math. Math. Phys. 43, 537–546 (2003). V. G. Romanov, Inverse Problems of Mathematical Physics (Nauka, Moscow, 1984) [in Russian]. T. K. Yuldashev, “Inverse problem for a nonlinear integro-differential equation of the third order,” Vestn. Samar. Univ., Ser. Estestv. Nauki, No. 1, 58–66 (2013). T. K. Yuldashev, “An inverse problem for nonlinear integro-differential equations of higher order,” Vestn. Voronezh. Univ., Fiz.Mat., No. 1, 153–163 (2014). T. K. Yuldashev, “Inverse problem for a partial Fredholm integro-differential equation of the third order,” J. Samar. Tekh. Univ., Ser. Fiz.Mat.Nauki 34 (1), 56–65 (2014). T. K. Yuldashev, “A certain Fredholm partial integro-differential equation of the third order,” Russ. Math. 59 (9), 62–66 (2015). T. K. Yuldashev, “A double inverse problem for a partial Fredholm integro-differential equation of fourth order,” Proc. JangjeonMath. Soc. 18, 417–426 (2015). T. K. Yuldashev, “Inverse problem for a nonlinear Benney-Luke type integro-differential equations with degenerate kernel,” Russ. Math. 60 (9), 53–60 (2016). V. A. Trenogin, Functional Analysys (Nauka, Moscow, 1980) [in Russian].