Abstract
In the present work, it is considered the features of solving classical Volterra-type integro-differential equations. Considered: features of the application of the Laplace transform; questions of stability and oscillations of solutions of integro-differential equations of the Volterra-type.
REFERENCES
Ya. V. Bykov, About Some Problems in the Theory of Integro-Differential Equations (Kirg. Gos. Univ., Frunze, 1957) [in Russian].
L. Levitov, Green’s Functions in Problems (Princeton Univ. Press, Princeton, 2011).
E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Part 1 (Princeton Univ. Press, Princeton, 1962).
A. I. Botashaev, Periodic Solutions of Volterra Integro-Differential Equations (Mosk. Fiz.-Tekh. Inst., Moscow, 1998) [in Russian].
Ya. V. Bykov and D. Ruzikulov, Periodic Solutions of Integro-Differential Equations and Their Asymptotics (Ilim, Frunze, 1986) [in Russian].
A. I. Egorov, ‘‘About the asymptotic behavior of solutions to systems of integro-differential equations of Volterra type,’’ Cand. Sci. (Phys.-Math.) Dissertation (Kirg. State Univ., Frunze, 1955).
S. Iskandarov and Z. A. Zhaparova, Specific Signs of Stability of Solutions of Linear Homogeneous Volterra Integro-Differential Equations of High Order (Inst. Math., Bishkek, 2022) [in Russian].
A. I. Egorov, ‘‘On the asymptotic behavior of solutions to systems of integro-differential equations of the Volterra type,’’ in Research in Mathematical Analysis and Mechanics in Uzbekistan, Collection of Articles (Akad. Nauk Uzb. SSR, Tashkent, 1960), pp. 114–126 [in Russian].
I. M. Babakov, Oscillation Theory (Tekh.-Teor. Liter., Moscow, 1958) [in Russian].
A. I. Egorov, Ordinary Differential Equations with Applications, 3rd ed. (Fizmatlit, Moscow, 2007) [in Russian].
T. K. Yuldashev, ‘‘Nonlocal boundary value problem for a nonlinear Fredholm integro-differential equation with degenerate kernel,’’ Differ. Equat. 54, 1646–1653 (2018).
T. K. Yuldashev, ‘‘Spectral features of the solving of a Fredholm homogeneous integro-differential equation with integral conditions and reflecting deviation,’’ Lobachevskii J. Math. 40, 2116–2123 (2019).
T. K. Yuldashev, ‘‘On inverse boundary value problem for a Fredholm integro-differential equation with degenerate kernel and spectral parameter,’’ Lobachevskii J. Math. 40, 230–239 (2019).
T. K. Yuldashev, ‘‘On the solvability of a boundary value problem for the ordinary Fredholm integrodifferential equation with a degenerate kernel,’’ Comput. Math. Math. Phys. 59, 241–252 (2019).
T. K. Yuldashev and S. K. Zarifzoda, ‘‘New type super singular integro-differential equation and its conjugate equation,’’ Lobachevskii J. Math. 41, 1123–1130 (2020).
Funding
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author of this work declares that he has no conflicts of interest.
Additional information
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
(Submitted by T. K. Yuldashev)
Rights and permissions
About this article
Cite this article
Egorov, A.I. Properties of Solutions to Volterra-Type Integro-Differential Equations. Lobachevskii J Math 44, 4240–4253 (2023). https://doi.org/10.1134/S1995080223100098
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080223100098