Sufficient conditions for the existence of solutions are obtained for a class of convolution-type integro-differential equations on the half line. The investigation is based on the three-factor decomposition of the initial integro-differential operator.
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A. V. Latishev and A. A. Yushkanov, “Exact solution of the problem of passage of current over the boundaries between crystals in metals,” FFT, 43, No. 10, 1744–1750 (2001).
A. V. Latishev and A. A. Yushkanov, “Electron plasma in semiinfinite metal in the presence of alternating electric fields,” Zh. Vych. Mat. Mat. Fiz., 41, No. 8, 1229–1241 (2001).
E. M. Livshits and L. P. Pitaevskii, Physical Kinetics [in Russian], Nauka, Moscow, Vol. 10 (1979).
Kh. A. Khachatryan, “Integro-differential equations of physical kinetics,” J. Contemp. Math. Anal., 39, No. 3, 49–57 (2004).
A. Kh. Khachatryan and Kh. A. Khachatryan, “On the solvability of some integro-differentials equation with sum-difference kernels,” Int. J. Pure Appl. Math. Sci. (India), 2, No. 1, 1–13 (2005).
Kh. A. Khachatryan, Ph. D. [in Russian], Yerevan (2005).
A. Kh. Khachatryan and Kh. A. Khachatryan, “On the structure of solution of one integro-differential equation with completely monotonic kernel,” in: Internat. Conf. on Harmonic Anal. and Approxim., Tsakhkadzor, Armenia (2005), pp. 42–43.
N. Wiener and N. Hopf, Über Eine Klasse Singularer Integral Eichungen Sitzing, Berlin (1931).
N. B. Yengibaryan and L. G. Arabajian, “Some factorization problems for integral operators of convolution type,” Differents. Uravn., 26, No. 8, 1442–1452 (1990).
A. N. Kolmogorov and V. S. Fomin, Elements of the Theory of Functions and Functional Analysis, Nauka, Moscow (1981).
L. G. Arabajian, “On one integral equation of the transport theory in inhomogeneous media,” Differents. Uravn., 23, No. 9, 1618–1622 (1987).
L. G. Arabajian and N. B. Yengibaryan, “Equations in convolutions and nonlinear functional equations,” Itogi VINITI., Mat. Anal., 175–242 (1984).
N. B. Yengibaryan and A. Kh. Khachatryan, “On some convolution-type integral equations in the kinetic theory,” Zh. Vych. Mat. Mat. Fiz., 38, No. 3, 466–482 (1998).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 11, pp. 1555–1567, November, 2008.
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Khachatryan, A.K., Khachatryan, K.A. Factorization of a convolution-type integro-differential equation on the positive half line. Ukr Math J 60, 1823–1839 (2008). https://doi.org/10.1007/s11253-009-0172-6
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DOI: https://doi.org/10.1007/s11253-009-0172-6