We study a class of vector convolution-type integrodifferential equations on the semiaxis used for the description of various applied problems of mathematical physics. By using a special three-factor decomposition of the original mathematical integrodifferential operator, we prove the solvability of these equations in certain functional spaces.
Similar content being viewed by others
References
E. M. Lifshits and L. M. Pitaevskii, Physical Kinetics [in Russian], Nauka, Moscow (1979).
J. D. Sargan, “The distribution of wealth,” Econometrica, No. 25, 568–590 (1957).
Kh. A. Khachatryan, “On some integrodifferential equations encountered in physical kinetics,” Izv. Akad. Nauk. Resp. Armen., Ser. Mat., 39, No. 3, 72–80 (2004).
A. V. Latyshev and A. A. Yushkanov, “Electron plasma in a semiinfinite metal in the presence of a variable electric field,” Zh. Vychisl. Mat. Mat. Fiz., 41, No. 8, 1229–1241 (2001).
A. Kh. Khachatryan and Kh. A. Khachatryan, “On the solvability of one boundary-value problem of physical kinetics,” Izv. Akad. Nauk. Resp. Armen., Ser. Mat., 41, No. 6, 65–74 (2004).
A. Kh. Khachatryan and Kh. A. Khachatryan, “On solvability of some integral-differential equation with sum-difference kernels,” Int. J. Pure Appl. Math. (India), 2, No. 1, 1–13 (2005).
A. Kh. Khachatryan and Kh. A. Khachatryan, “On the structure of solution of one integral-differential equation with completely monotonic kernel,” in: Proc. of the Internat. Conf. “Harmonic Analysis and Approximations” (2005), pp. 42–43.
A. Kh. Khachatryan and Kh. A. Khachatryan, “On the problem of solvability of an integrodifferential equation with almost sumdifference kernel,” Mat. Vyssh. Shkol., 2, No. 4, 26–31 (2006).
N. Wiener and N. Hopf, Über Eine Klasse Singularer Integral Eichungen Sitzig, Berlin (1931), pp. 696–706.
L. G. Arabadzhyan and N. B. Engibaryan, “Convolution equations and nonlinear functional equations,” Itogi VINITI, Ser. Mat. Anal. [in Russian], Vol. 22, VINITI, Moscow (1984), pp. 175–242.
N. B. Engibaryan and A. A. Arutyunyan, “Integral equations on a half line with difference kernels and nonlinear functional equations,” Mat. Sb., 97, 35–58 (1975).
N. B. Engibaryan and L. G. Arabadzhyan, “Some problems of factorization for integral convolution-type operators,” Differents. Uravn., 26, No. 8, 1442–1452 (1990).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, [in Russian], Nauka, Moscow (1981).
I. P. Natanson, Theory of Functions of Real Variable [in Russian], Nauka, Moscow (1974).
G. M. Fikhtengol’ts, A Course of Differential and Integral Calculus [in Russian], Vol. 2, Nauka, Moscow (1966).
L. G. Arabadzhyan, “On one integral equation of the transport theory in inhomogeneous media,” Differents. Uravn., 23, No. 9, 1618–1622 (1987).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 9, pp. 1277–1292, September, 2009.
Rights and permissions
About this article
Cite this article
Khachatryan, A.K., Khachatryan, K.A. On some systems of convolution-type first-order integrodifferential equations on the semiaxis. Ukr Math J 61, 1511–1528 (2009). https://doi.org/10.1007/s11253-010-0293-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-010-0293-y