Functional-differential equations in Sobolev spaces and related problems of spectral theory
V. V. Vlasov, D. A. Medvedev

This publication is cited in the following articles:

1. Yu. N. Orlov, V. Zh. Sakbaev, “Feynman–Kac formulas for solutions of evolution equations. Part II. Evolution families and functional integrals”, jour, 4:4 (2026), 136  
2. N. V. Zaitseva, “Classical solutions of multidimensional hyperbolic equations with incommensurate translations in lower-order derivatives”, Math. Notes, 119:1 (2026), 29–34      
3. N. V. Zaitseva, “Klassicheskie resheniya giperbolicheskikh uravnenii v poluprostranstve s operatorom sdviga v mladshikh proizvodnykh”, Izv. vuzov. Matem., 2026, no. 1, 18–24    
4. N. V. Zaitseva, “Classical Solutions of Hyperbolic Equations in a Half-Space with a Translation Operator in Lower-Order Derivatives”, Russ Math., 70:1 (2026), 15  
5. Eugene Bravyi, “On the surjectivity conditions of a linear functional differential operator of the second order”, Electron. J. Qual. Theory Differ. Equ., 2025, no. 11, 1  
6. V. A. Sadovnichy, E. A. Baderko, T. P. Lukashenko, N. A. Rautian, T. V. Rodionov, I. Kh. Sabitov, V. G. Chirskii, V. B. Sherstyukov, “Research activity of the Chair of Mathematical Analysis”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 80:1 (2025), 67–71        
7. N. V. Zaitseva, “Model Problem in a Strip for a Hyperbolic Differential-Difference Equation”, Diff Equat, 61:1 (2025), 1  
8. Marko Kostić, “Almost periodic-type functions and their applications: Survey of recent results and further perspectives”, Journal of Applied Analysis, 2025  
9. N. V. Zaitseva, “Classical Solutions of One Multidimensional Hyperbolic Equation with Incommensurable Translations in Lower Derivatives”, Diff Equat, 61:4 (2025), 542  
10. N. V. Zaitseva, “Classical Solutions of Hyperbolic Equations with Translation Operators in Lower-Order Derivatives”, Diff Equat, 61:5 (2025), 627  
11. N. V. Zaitseva, “Solution of the Cauchy Problem for a Hyperbolic Equation with a Nonlocal Potential”, Diff Equat, 61:6 (2025), 849  
12. Vladimir Vasilyev, Natalya Zaitseva, “On Hyperbolic Equations with a Translation Operator in Lowest Derivatives”, Mathematics, 12:12 (2024), 1896  
13. Yu. N. Orlov, V. Z. Sakbaev, “Feynman–Kac Formulas for Difference-differential Equations of Retarded Type”, Lobachevskii J Math, 45:6 (2024), 2567  
14. N. V. Zaitseva, “Classical Solutions of Hyperbolic Differential-Difference Equations”, Diff Equat, 60:7 (2024), 817  
15. O. V. Solonukha, “Nonlinear Differential-Difference Equations of Elliptic and Parabolic Type and Their Applications to Nonlocal Problems”, J Math Sci, 2024  
16. N. V. Zaitseva, “On the Existence of Smooth Solutions to a Hyperbolic Differential-Difference Equation”, Diff Equat, 60:9 (2024), 1153  
17. O. V. Solonukha, “Nelineinye differentsialno-raznostnye uravneniya ellipticheskogo i parabolicheskogo tipa i ikh prilozheniya k nelokalnym zadacham”, SMFN, 69, no. 3, Rossiiskii universitet druzhby narodov, M., 2023, 445–563    
18. N. V. Zaitseva, A. B. Muravnik, “Smooth Solutions of Hyperbolic Equations with Translation by an Arbitrary Vector in the Free Term”, Diff Equat, 59:3 (2023), 371  
19. Vladimir Vasilyev, Natalya Zaitseva, “Classical Solutions of Hyperbolic Equation with Translation Operators in Free Terms”, Mathematics, 11:14 (2023), 3137  
20. Natalya V. Zaitseva, Springer Proceedings in Mathematics & Statistics, 423, Differential Equations, Mathematical Modeling and Computational Algorithms, 2023, 289  
21. N. V. Zaitseva, “On One Cauchy Problem for a Hyperbolic Differential-Difference Equation”, Diff Equat, 59:12 (2023), 1787  
22. N. V. Zaitseva, A. B. Muravnik, “Classical solutions of hyperbolic differential-difference equation with shift by an arbitrary vector”, Russian Math. (Iz. VUZ), 67:5 (2023), 29–34      
23. A. B. Muravnik, N. V. Zaitseva, “Classical Solutions of Hyperbolic Differential-Difference Equations with Differently Directed Translations”, Lobachevskii J Math, 44:3 (2023), 920  
24. N. V. Zaitseva, “Classical Solutions of a Multidimensional Hyperbolic Differential–Difference Equation with Shifts of Various Directions in the Potentials”, Math. Notes, 112:6 (2022), 872–880        
25. Vladimir Vasilyev, Natalya Zaitseva, “Initial Problem for Two-Dimensional Hyperbolic Equation with a Nonlocal Term”, Mathematics, 11:1 (2022), 130  
26. N. V. Zaitseva, “Hyperbolic differential-difference equations with nonlocal potentials”, Ufa Math. J., 13:3 (2021), 36–43      
27. N. V. Zaitseva, “Classical solutions of hyperbolic equations with nonlocal potentials”, Dokl. Math., 103:3 (2021), 127–129          
28. N. V. Zaitseva, “Classical Solutions of Hyperbolic Differential–Difference Equations in a Half-Space”, Diff Equat, 57:12 (2021), 1629  
29. G. V. Demidenko, I. I. Matveeva, Springer Proceedings in Mathematics & Statistics, 379, Functional Differential Equations and Applications, 2021, 145  
30. Luciano Pandolfi, Interdisciplinary Applied Mathematics, 54, Systems with Persistent Memory, 2021, 103  
31. Luciano Pandolfi, Interdisciplinary Applied Mathematics, 54, Systems with Persistent Memory, 2021, 1  
32. Luciano Pandolfi, Interdisciplinary Applied Mathematics, 54, Systems with Persistent Memory, 2021, 163  
33. N. V. Zaitseva, “Classical Solutions of Hyperbolic Differential-Difference Equations with Several Nonlocal Terms”, Lobachevskii J Math, 42:1 (2021), 231  
34. O. V. Solonukha, “The First Boundary Value Problem for Quasilinear Parabolic Differential-Difference Equations”, Lobachevskii J Math, 42:5 (2021), 1067  
35. Zaitseva V N., “Global Classical Solutions of Some Two-Dimensional Hyperbolic Differential-Difference Equations”, Differ. Equ., 56:6 (2020), 734–739          
36. N. V. Zaitseva, “On global classical solutions of hyperbolic differential-difference equations”, Dokl. Math., 101:2 (2020), 115–116          
37. Clement McCalla, “On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations”, Mathematics, 8:9 (2020), 1418  
38. N. A. Karazeeva, “Asymptotic Behavior and Attractor of Systems Governing Two-Dimensional Viscoelastic Flows”, J Math Sci, 242:1 (2019), 149  
39. V. V. Vlasov, N. A. Rautian, “Issledovanie operatornykh modelei, voznikayuschikh v teorii vyazkouprugosti”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 60–73    
40. Burlutskaya M.Sh., Khromov A.P., “Dirac Operator With a Potential of Special Form and With the Periodic Boundary Conditions”, Differ. Equ., 54:5 (2018), 586–595          
41. J. Math. Sci. (N. Y.), 238:5 (2019), 652–657    
42. Vlasov V.V. Rautian N.A., “Study of Functional-Differential Equations With Unbounded Operator Coefficients”, Dokl. Math., 96:3 (2017), 620–624        
43. Sgibnev M.S., “Asymptotic Expansion of the Solution of a Matrix Differential-Difference Equation of the General Form”, Differ. Equ., 52:1 (2016), 28–38            
44. V. V. Vlasov, N. A. Rautian, “Spektralnyi analiz integrodifferentsialnykh uravnenii v gilbertovom prostranstve”, Trudy seminara po differentsialnym i funktsionalno-differentsialnym uravneniyam v RUDN pod rukovodstvom A. L. Skubachevskogo, SMFN, 62, RUDN, M., 2016, 53–71  
45. N. A. Rautian, V. V. Vlasov, Springer Proceedings in Mathematics & Statistics, 164, Differential and Difference Equations with Applications, 2016, 411  
46. V. V. Vlasov, N. A. Rautian, “Well-posed solvability of volterra integro-differential equations in Hilbert space”, Diff Equat, 52:9 (2016), 1123  
47. A. Yaakbarieh, V. Zh. Sakbaev, “Correctness of a problem with initial conditions for parabolic differential-difference equations with shifts of time argument”, Russian Math. (Iz. VUZ), 59:4 (2015), 13–19    
48. D. A. Zakora, “Operator approach to the ilyushin model for a viscoelastic body of parabolic type”, Journal of Mathematical Sciences, 225:2 (2017), 345–381    
49. V. V. Vlasov, N. A. Rautian, “Well-posedness and spectral analysis of integrodifferential equations arising in viscoelasticity theory”, Journal of Mathematical Sciences, 233:4 (2018), 555–577    
50. R. K. Romanovsky, E. M. Nazaruk, “Dichotomy of solutions of differential-difference equations in a Sobolev space”, Dokl. Math., 91:2 (2015), 193  
51. Sascha Trostorff, “On integro‐differential inclusions with operator‐valued kernels”, Math Methods in App Sciences, 38:5 (2015), 834  
52. V. V. Vlasov, N. A. Rautian, “Spectral analysis of hyperbolic Volterra integro-differential equations”, Dokl. Math., 92:2 (2015), 590  
53. L. A. Vlasenko, A. G. Rutkas, “On a Class of Impulsive Functional-Differential Equations with Nonatomic Difference Operator”, Math. Notes, 95:1 (2014), 32–42            
54. M. S. Sgibnev, “Behavior at infinity of a solution to a matrix differential-difference equation”, Siberian Math. J., 55:3 (2014), 530–543            
55. R. K. Romanovsky, E. M. Nazaruk, “Lyapunov's direct method for linear systems of functional-differential equations in Sobolev space”, Siberian Math. J., 55:4 (2014), 696–705        
56. Vlasov V.V. Rautian N.A., “Spectral Analysis and Representations of Solutions to Abstract Integrodifferential Equations”, Dokl. Math., 89:1 (2014), 34–37            
57. A. B. Muravnik, “Functional differential parabolic equations: integral transformations and qualitative properties of solutions of the Cauchy problem”, Journal of Mathematical Sciences, 216:3 (2016), 345–496    
58. V. V. Vlasov, N. A. Rautian, “Properties of solutions of integro-differential equations arising in heat and mass transfer theory”, Trans. Moscow Math. Soc., 75 (2014), 185–204      
59. Akylzhanov R.Kh., Vlasov V.V., “Well-Posed Solvability of Functional-Differential Equations With Unbounded Operator Coefficients”, Differ. Equ., 50:9 (2014), 1161–1172            
60. Sgibnev M.S., “Asymptotic Expansion of the Solution of a Differential-Difference Equation of General Form”, Differ. Equ., 50:3 (2014), 323–334            
61. Victor V. Vlasov, Nadezda A. Rautian, Operator Theory: Advances and Applications, 236, Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation, 2014, 517  
62. Jana Hrabalová, Jan Čermák, “Delay-dependent stability criteria for neutral delay differential and difference equations”, DCDS-A, 34:11 (2014), 4577  
63. V. V. Vlasov, N. A. Rautian, “On the asymptotic behavior of solutions of integro-differential equations in a Hilbert space”, Diff Equat, 49:6 (2013), 718  
64. G. M. Sklyar, P. Polak, “Asymptotic Growth of Solutions of Neutral Type Systems”, Appl Math Optim, 67:3 (2013), 453  
65. V. V. Vlasov, N. A. Rautian, “Integrodifferential equations in viscoelasticity theory”, Russian Math. (Iz. VUZ), 56:6 (2012), 48–51      
66. V. V. Vlasov, “On some classes of integro-differential equations on the half-line and related operator functions”, Trans. Moscow Math. Soc., 73 (2012), 121–138        
67. V. V. Vlasov, N. A. Rautian, A. S. Shamaev, “Analysis of operator models arising in problems of hereditary mechanics”, Journal of Mathematical Sciences, 201:5 (2014), 673–692      
68. M. S. Sgibnev, “Behavior at infinity of a solution to a differential-difference equation”, Siberian Math. J., 53:6 (2012), 1139–1154            
69. V. V. Vlasov, N. A. Rautian, A. S. Shamaev, “Spectral analysis and correct solvability of abstract integrodifferential equations arising in thermophysics and acoustics”, Journal of Mathematical Sciences, 190:1 (2013), 34–65      
70. N. A. Rautian, “On the Structure and Properties of Solutions of Integro-Differential Equations Arising in Thermal Physics and Acoustics”, Math. Notes, 90:3 (2011), 455–459          
71. V. V. Vlasov, N. A. Rautian, “Well-defined solvability and spectral analysis of abstract hyperbolic integrodifferential equations”, J. Math. Sci. (N. Y.), 179:3 (2011), 390–414        
72. A. A. Gavrikov, A. S. Shamaev, “Some problems in acoustics of emulsions”, J. Math. Sci. (N. Y.), 179:3 (2011), 415–436        
73. V. V. Vlasov, J. Wu, G. R. Kabirova, “Well-defined solvability and spectral properties of abstract hyperbolic equations with aftereffect”, Journal of Mathematical Sciences, 170:3 (2010), 388–404      
74. Vlasov V.V., Rautian N.A., Shamaev A.S., “Solvability and Spectral Analysis of Integro-Differential Equations Arising in the Theory of Heat Transfer and Acoustics”, Dokl. Math., 82:2 (2010), 684–687                
75. Vlasov V.V., Wu J., “Spectral analysis and solvability of abstract hyperbolic equations with aftereffect”, Differ. Equ., 45:4 (2009), 539–548