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Generalized Solutions of Volterra Integral Equations of the First Kind

Sidorov, N.A., and Falaleev, M.V., and Sidorov, D.N., (2006) Generalized Solutions of Volterra Integral Equations of the First Kind. Bulletin of the Malaysian Mathematical Sciences Society, 29 (2). pp. 101-109. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v29n2/v29n2p1.pdf

Affiliations

Irkutsk State University, Faculty of Mathematics
Siberian Branch of Russian Academy of Sciences, Institute of Energy Systems

Abstract

Volterra integral equations of the first kind are studied in terms of generalized functions. The solutions consist of singular and regular components which can be constructed separately. The singular component is constructed as solution of the special linear algebraic system. The regular component is constructed as solution of the special Volterra integral equation of the third kind.

Item Type:Journal
Keywords:Distribution space, Volterra integral equations, Dirac function, impulses theory.
Subjects:Q Science, Computer Science
ID Code:1438

[1] A. S. Apartsyn, Nonclassical Linear Volterra Equations of the First Kind , VSP Brill Academic Publishers, Zeist, 2003.

[2] A. S. Apartsin, S. V. Solodusha, Test signal amplitude optimization for identification of the Volterra kernels, Automation and Remote Oontrol J. 65 (3) (2004), 464-471.

[3] V. Dolexal, Dynamics of Linear Systems, Academia, Prague, 1967.

[4] M. V. Falaleev, Fundamental operator-functions of the singular differential operators in the the Banach spaces, Sib. Math. J. 41(5) (2000), 1167-1182 (in Russian); Transl. in Sib. Math. J. 41 (2000) 960-973.

[5] A. D. Mishkis, New proof of the generalized solution of the integral equation of the first kind of the general case, in: Integral-Differential Equations Studies, Ilim Publ., Frunze, 1983, (in Russian).

[6] D. N. Sidorov, Modelling of non-linear dynamic systems by volterra series approach method: identification and applications, in: Attractors, Signals, and Synergetics, W. Klonowski, ed., Pabst Science Publ., Berlin, 2002, 276—282.

[7] N. A. Sidorov, M. V. Falaleev, Generalized Solutions of the Volterra Integral Equations of the First Kind, in: Proc. of XII Baikal International Conference Optimization Methods and its Applications. Vol. 4 (ISDCT Publ., Irkutsk, 2001) 173-177 (in Russian).

[8] N. Sidorov, B. Loginov, A. Sinitsyn, M. Falaleev, Lyapunov-Schmidt Methods in Nonlinear Analysis ond Applications, Kluwer Academic Publishers, Dordrecht, 2002.

[9] N. A. Sidorov, D. N. Sidorov, Solvabolity of the Volterra integral equations of the first kind in the space of generalized functions, J. Optimization, Control and Intelligence 5 (ISDCT Publ., Irkutsk) (2000), 80-85 (in Russian).

[10] S. V. Vladimirov, Mathematical Physics Equations, Mir Publ., 1984 (originally published in Russian by Nauka Publ., 1981.)

[11] S. T. Zavalishchin, A. N. Sesekin, Dynamic Impulse Systems. Theory and Applications, Kluwer Academic Publishers, Dordrecht, 1997.

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