Theory of linear abstract functional differential equations and applications

Memoirs on Differential Equations and Mathematical Physics

Volumn 8, Issue , 1996, Pages 1-102

  Azbelev, N V ^a   Rakhmatullina, L F ^a  

^a PERM NATIONAL RESEARCH POLYTECHNIC UNIVERSITY   (Russian Federation)

Author keywords

Boundary value problem; Green operator; Linear operator; Noether operator

Indexed keywords

EID: 0042593777     PISSN: 15120015     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (44)

1. N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the theory of functional differential equations. (Russian) Nauka, Moscow, 1991.
2. N. V. Azbelev and G. G. Islamov, To the theory of abstract linear equation. (Russian) In: Funktsional'no-differentsial'nye Uravneniya. Perm, 1989, 3-16.
3. I. V. Shragin, The Nemytsky abstract operator as locally defined operator. (Russian) Dokl. Akad. Nauk SSSR 227(1976), No. 1, 47-49.
4. A. V. Ponosov, On Nemytsky hypothesis. (Russian) Dokl. Akad. Nauk SSSR 289(1986), No. 6, 1308-1311.
5. S. G. Krein, Linear equations in Banach space. (Russian) Nauka, Moscow, 1971.
6. L. V. Kantorovich and G. P. Akilov, Functional analysis. (Rus-sian) Nauka, Moscow, 1977.
7. V. P. Maksimov, Noether property of the general boundary value problem for linear functional differential equation. (Russian) Differentsial'nye Uravneniya 10(1974), No. 12, 2288-2291.
8. N. V. Azbelev, L. F. Rakhmatullina, and A. G. Terentiev, W-method in studying of differential equations with deviated argument. (Russian) Trudy Inst. Khimicheskogo Mashinostroeniya, Tambov, 1970. 60-63.
9. M. M. Vainberg and V. A. Trenogin, Bifurcation theory of nonlinear equations. (Russian) Nauka, Moscow, 1969.
10. V. P. Plaksina, Some questions in the theory of impulse boundary value problem. (Russian) Dissertation. Perm, 1989.
11. L. F. Rakhmatullina, Generalized Green's operator of the overde-termined boundary value problem for linear functional differential equations. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. (1993), No. 5, 95-100.
12. Ja. Kurzweil, On continuous dependence on parameter in the theory of ordinary differential equations and on the generalization of the concept of differential equations. (Russian) Uspekhi Mat. Nauk 12(1957), No. 5, 257-259.
13. G. M. Vainikko, Regular convergence of operators and approximate solution of equations. (Russian) Itogi nauki i techniki. Ser. matematicheskiĭ analiz 16(1979), 5-53.
14. A. V. Anokhin, On continuous dependence of the solution of abstract functional differential equation on parameters. (Russian) In: Funktsional'no-differentsial'nye Uravneniya. Perm, 1990, 142-145.
15. N. V. Azbelev, M. P. Berdnikova, and L. F. Rakhmatullina, Integral equations with deviated argument. (Russian) Dokl. Akad. Nauk SSSR 192(1970), No. 3, 479-482.
16. N. V. Azbelev and L. F. Rakhmatullina, On linear equations with deviated argument. (Russian) Differentsial'nye Uravneniya 6(1970), No. 4, 616-628.
17. A. D. Myshkis, Linear differential equations with delay argument. (Russian) Nauka, Moscow, 1965.
18. N. Dunford and J. T. Schvarz, Linear operators. General theory, Wiley-Interscience, 1961.
19. M. E. Drakhlin and T. K. Plyshevskaya, On the theory of functional differential equations. (Russian) Differentsial'nye Uravneniya 14(1978), No. 8, 1347-1361.
20. M. E. Drakhlin, The composition operator in the space of summable functions. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. (1986), No. 5, 18-23.
21. A. V. Chistyakov, Pathological counterexample to the hypothesis about lack of Fredholm property in the algebras of operators of weighted shift. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. (1995), No. 10, 76-86.
22. N. V. Azbelev, Two hypotheses in the theory of functional differential equations. (Russian) Uspekhi Mat. Nauk 41(1986), No. 4, 210-211.
23. N. V. Azbelev, L. M. Berezanskiĭĭ, and L. F. Rakhmatullina, On linear functional differential equation of the evolutional type. (Russian) Differentsial'nye Uravneniya 13(1977), No. 11. 1915-1925.
24. A. V. Anokhin, On linear impulse system for functional differential equations. (Russian) Dokl. Akad. Nauk SSSR 286(1986), No. 5, 1037-1040.
25. N. N. Likhacheva, On differential inequalities for equations with deviated argument. (Russian) Perm Polytechnical Institute, Perm, 1989. 16 pp. Dep. in VINITI 04.04.89, N 2467-89.
26. T. A. Osechkina, Periodical boundary value problem for functional differential equation. (Russian) Dissertation, Perm, 1994.
27. A. I. Shindyapin, On a boundary value problem for a singular equation. (Russian) Differenstial'nye Uravneniya 20(1984), No. 3, 450-455.
28. M. E. Drakhlin and L. M. Kultysheva, On composition operator in the spaces of Orlicz. (Russian) In: Boundary value problems. Perm, 1977. 126-130.
29. E. I. Bravi, On regularization of singular functional differential equations. (Russian) Differentsial'nye Uravneniya 30(1994), No. 1. 26-34.
30. E. I. Bravi, On solvability of a boundary value problem for a nonlinear singular functional differential equation. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. (1993), No. 5. 17-23.
31. S. M. Labovskiĭĭ, Positive solutions of a two-point boundary value problem for a linear singular functional differential equation. (Russian) In: Funktsional'no-differentsial'nye Uravneniya, Perm, 1985, 35-49.
32. I. T. Kiguradze, Some singular boundary value problems for ordinary differential equations. (Russian) Tbilisi University Press, Tbilisi, 1975.
33. I. T. Kiguradze and B. L. Shekhter, Singular boundary value problems for ordinary differential equations. Itogi nauki i techniki. Ser. Sovremennye problemy matematiki: novye dostizheniya 30(1987), 105-201.
34. V. M. Alekseev, E. M. Galeev, and V. M. Tikhomirov, Collection of problems on optimization. Theory. Examples. Problems. (Russian) Nauka, Moscow, 1984.
35. M. E. Drakhlin and M. A. Makagonova, Euler functional differential equations. (Russian) In: Funktsional'no-differentsial'nye Uravneniya, Perm, 1987, 12-18.
36. A. A. Gruzdev, On reduction of extremal problem to linear equation in optimization theory. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. (1993), No. 6, 40-47.
37. A. A. Gruzdev and S. A. Gusarenko, On reduction of variational problem to the extremal problem without restrictions. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. (1994) No. 6, 39-50.
38. N. V. Azbelev, Recent state and trends of developing of the theory of functional differential equations. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. (1994) No. 6, 8-19.
39. G. G. Islamov, On an upper estimate of the spectral radius. (Rus-sian) Dokl. Akad. Nauk SSSR 322(1992), No. 5, 836-838.
40. M. A. Korytova, On estimate of the spectral radius of some linear operators. (Russian) In: Funktsional'no-differentsial'nye Uravneniya, Perm, 1992, 239-245.
41. V. Zeidan and Z. Pierluigi, Coupled points in the calculus of variations and applications to periodic problems. Trans. Amer. Math. Soc. 315(1989), No. 1, 323-335.
42. L. D. Kudryavtsev, On existence and uniqueness of solutions of variational problems. (Russian) Dokl. Akad. Nauk SSSR. 298(1988), No. 5, 1055-1060.
43. N. V. Azbelev and A. I. Domoshnitskiĭ, On the differential inequality of Vallée-Poussin. (Russian) Differentsial'nye Uravneniya 22(1986), No. 12, 2041-2045.
44. N. V. Azbelev and L. F. Rakhmatullina, On extension of the Vallée-Poussin theorem to equations with aftereffect. (Russian) In: Boundary Value Problems for Functional Differential Equations, World Scientific, 1995, 23-36.