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Mat. Zametki, 2014, Volume 96, Issue 5, Pages 773–789 (Mi mz10220)  

This article is cited in 15 scientific papers (total in 15 papers)

On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels

N. A. Sidorova, D. N. Sidorovabc

a Irkutsk State University
b L. A. Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences
c National Research Irkutsk State Technical University

Abstract: We obtain sufficient conditions for the existence and uniqueness of continuous solutions of Volterra operator equations of the first kind with piecewise determined kernels. For the case in which the solution is not unique, we prove existence theorems for the parametric families of solutions and present their asymptotics in the form of logarithmic polynomials.

Keywords: Volterra operator equation, Banach space, asymptotic approximation, successive approximation method, Fredholm point, Fredholm operator, Jordan set.

DOI: https://doi.org/10.4213/mzm10220

Full text: PDF file (570 kB)
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English version:
Mathematical Notes, 2014, 96:5, 811–826

Bibliographic databases:

UDC: 517.968.22
Received: 09.10.2012
Revised: 30.11.2013

Citation: N. A. Sidorov, D. N. Sidorov, “On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels”, Mat. Zametki, 96:5 (2014), 773–789; Math. Notes, 96:5 (2014), 811–826

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Syed T.A., Krishnan V.P., Sivaswamy J., “Numerical Inversion of Circular Arc Radon Transform”, IEEE Trans. Comput. Imaging, 2:4 (2016), 540–549  crossref  mathscinet  isi
    2. P. J. Davies, D. B. Duncan, “Numerical approximation of first kind Volterra convolution integral equations with discontinuous kernels”, J. Integral Equations Appl., 29:1 (2017), 41–73  crossref  mathscinet  zmath  isi  scopus
    3. P. Assari, M. Dehghan, “A meshless local discrete Galerkin (mldg) scheme for numerically solving two-dimensional nonlinear Volterra integral equations”, Appl. Math. Comput., 350 (2019), 249–265  crossref  mathscinet  isi  scopus
    4. N. A. Sidorov, “Classic solutions of boundary value problems for partial differential equations with operator of finite index in the main part of equation”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 27 (2019), 55–70  mathnet  crossref
    5. S. Noeiaghdam, D. N. Sidorov, I. R. Muftahov, A. V. Zhukov, “Control of accuracy on Taylor-collocation method for load leveling problem”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 30 (2019), 59–72  mathnet  crossref
    6. N. Sidorov, D. Sidorov, Y. Li, “Nonlinear systems' equilibrium points: branching, blow-up and stability”, All-Russian Conference and School For Young Scientists, Devoted to 100Th Anniversary of Academician l.V. Ovsiannikov - Mathematical Problems of Continuum Mechanics, Journal of Physics Conference Series, 1268, IOP Publishing Ltd, 2019, 012065  crossref  mathscinet  isi
    7. A. Tynda, D. Sidorov, I. Muftahov, “Numerical analysis of fractional order integral dynamical models with piecewise continuous kernels”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 13:4 (2020), 58–65  mathnet  crossref
    8. Sidorov D., Tynda A., Muftahov I., Dreglea A., Liu F., “Nonlinear Systems of Volterra Equations With Piecewise Smooth Kernels: Numerical Solution and Application For Power Systems Operation”, Mathematics, 8:8 (2020), 1257  crossref  isi
    9. S. K. Zarifzoda, R. N. Odinaev, “Issledovanie nekotorykh klassov integro-differentsialnykh uravnenii v chastnykh proizvodnykh vtorogo poryadka so stepenno-logarifmicheskoi osobennostyu v yadre”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2020, no. 67, 40–54  mathnet  crossref
    10. Sidorov V N., Teplyakova N.A., Palatnikov M.N., Aleshina L.A., Sidorova V O., Kadetova V A., “Raman Spectroscopy and X-Ray Analysis of Non-Stoichiometric Lithium Niobate Crystals”, J. Solid State Chem., 282 (2020), 121109  crossref  isi
    11. Noeiaghdam S., Sidorov D., Sizikov V., Sidorov N., “Control of Accuracy of Taylor-Collocation Method to Solve the Weakly Regular Volterra Integral Equations of the First Kind By Using the Cestac Method”, Appl. Comput. Math., 19:1 (2020), 87–105  mathscinet  isi
    12. Falaleev V M., Romanova O.A., Sinitsyn V A., Dreglea I A., Leont'ev R.Yu., Sidorov D.N., “On the Occasion of the 80Th Birthday of Professor N. a. Sidorov”, Bull. Irkutsk State Univ.-Ser. Math., 32 (2020), 134–143  crossref  mathscinet  isi
    13. Sidorov N., Sidorov D., Dreglea A., “Solvability and Bifurcation of Solutions of Nonlinear Equations With Fredholm Operator”, Symmetry-Basel, 12:6 (2020), 912  crossref  isi
    14. N. A. Sidorov, A. I. Dreglya, “Differentsialnye uravneniya v banakhovykh prostranstvakh s neobratimym operatorom v glavnoi chasti i neklassicheskimi nachalnymi usloviyami”, Differentsialnye uravneniya i optimalnoe upravlenie, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 183, VINITI RAN, M., 2020, 120–129  mathnet  crossref
    15. Noeiaghdam S., Sidorov D., Wazwaz A.-M., Sidorov N., Sizikov V., “The Numerical Validation of the Adomian Decomposition Method For Solving Volterra Integral Equation With Discontinuous Kernels Using the Cestac Method”, Mathematics, 9:3 (2021), 260  crossref  isi
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