Skip to main content
Log in

Multilinear Volterra Equations of the First Kind

  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The Lambert function is used to derive unimprovable estimates for the solutions of nonlinear integral inequalities that play a pivotal role in the study of multilinear Volterra equations of the first kind.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. Apartsyn, A.S., Mathematical Modelling of Dynamic Systems and Objects with the Help of the Volterra Integral Series, EPRI-SEI Joint seminar, Beijing, China, 1991, pp. 117-132.

  2. Apartsyn, A.S., On Some Identification Method for Nonlinear Dynamic Systems, ISEMA-92, Shenzhen, China, 1992, pp. 288-292.

  3. Apartsyn, A.S., New Classes of Linear Multidimensional Volterra Equations of the First Kind, Izv.Vuzov, Mat., 1995, no. 11, pp. 28-41.

    Google Scholar 

  4. Brunner, H. and van der Houwen, P.J., The Numerical Solution of Volterra Equations, Amsterdam: North-Holland, 1986.

    Google Scholar 

  5. Krasnosel'skii, M.A., Topologicheskie metody v teorii nelineinykh integral'nykh uravnenii, Moscow: Gostekhizdat, 1956. Translated under the title Topological Methods in the Theory of Nonlinear Integral Equations, Oxford: Pergamon, 1964.

    Google Scholar 

  6. Krasnosel'skii, M.A., Polozhitel'nye resheniya operatornykh uravnenij (Positive Solutions of Operator Equations), Moscow: Fizmatgiz, 1962.

    Google Scholar 

  7. Krasnosel'skii, M.A., Vainikko, G.M., Zabreiko, P.P., et al., Priblizhennoe reshenie operatornykh uravnenii, Moscow: Nauka, 1969. Translated under the title Approximate Solutions of Operator Equations, Groningen: Walters-Noordhoff, 1972.

    Google Scholar 

  8. Hutson, V. and Pym, J.G., Applications of Functional Analysis and Operator Theory, London: Academic, 1980. Translated under the title Prilozheniya funktsional'nogo analiza i teorii operatorov, Moscow: Mir, 1983.

    Google Scholar 

  9. Trenogin, V.A., Funktsional'nyi analiz (Functional Analysis), Moscow: Nauka, 1980.

    Google Scholar 

  10. Volterra, V., Theory of Functionals and of Integral and Integro-differential Equations, London: Blackie & Son, 1930. Translated under the title Teoriya funktsionalov, integral'nykh i integro-di-erentsial'nykh uravnenii, Moscow: Nauka, 1982.

    Google Scholar 

  11. Apartsyn, A.S., Neklassicheskie uravneniya Vol'terra I roda.Teoriya i chislennye metody (Nonclassical Volterra Equations of the First Kind. Theory and Numerical Methods), Novosibirsk: Nauka, 1999.

    Google Scholar 

  12. Corless, R.M., Gonnet, G.H., Hare, D.E., Jeffrey, D.J., and Knuth, D.E., On the Lambert W Function, Adv.Comput.Math., 1996, vol. 5, pp. 329-359.

    Google Scholar 

  13. Apartsyn, A.S. and Markova, E.V., A Numerical Solution of the Multilinear Volterra Equations of the First Kind by the Cubature Method, Mat.VI Mezhdunar.seminara-soveshchaniya “Kubaturnye formuly i ikh prilozheniya” (Int. Conference “Cubature Formulas and Their Application), Ufa: Vychisl. Tsentr, 2001, pp. 5-9.

    Google Scholar 

  14. Apartsyn, A.S. and Markova, E.V., A Numerical Solution of the Bilinear Volterra Equations of the First Kind by the Cubature Method, Trudy XII Baikal'skoi mezhdunar.konf.“Metody optimizatsii i ikh prilozheniya” (Proc. XII Baikal Int. Conf. “Optimization Methods and Their Applications”), Irkutsk, 2001, vol. 4, pp. 20-24.

    Google Scholar 

  15. Apartsyn, F.S. and Markova, E.V., On Numerical Solution of the Multilinear Volterra Equations of the First Kind, Proc.Int.Conf.Comput.Mat., Novosibirsk: ICM & MG, 2002, part 2, pp. 322-326.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Apartsyn, A.S. Multilinear Volterra Equations of the First Kind. Automation and Remote Control 65, 263–269 (2004). https://doi.org/10.1023/B:AURC.0000014723.06564.f4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:AURC.0000014723.06564.f4

Keywords

Navigation