Geodesic
To estimating linear functionals values over solutions of systems with aftereffect
Vestnik rossijskih universitetov. Matematika, Tome 25 (2020) no. 131, pp. 274-283
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a wide class of linear functional differential systems with Volterra operators, a constructive technique is proposed to obtain estimates of linear functionals values over solutions in conditions of uncertainty of external perturbations. It can be applied to solutions of boundary value problems with arbitrary number of boundary conditions as well as to description of attainability sets in control problems with respect to given on-target functionals. External perturbations are constrained by a given linear inequalities system on the main time segment. The technique is based on the results of general theory of functional differential equations about the solvability of boundary value problems with general linear boundary conditions and the representation of solutions. The problem under consideration is reduced to the generalized moment problem. Therewith the results on the properties of the Cauchy matrix to systems with aftereffect are of essential importance. The general form of functionals allows one to cover many cases being topical in applications such as multipoint, integral ones, as well as hybrids of those.
Keywords: functional differential equations, systems with aftereffect, boundary value problems, estimating solutions. 
@article{VTAMU_2020_25_131_a2,
     author = {V. P. Maksimov},
     title = {To estimating linear functionals values over solutions of systems with aftereffect},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {274--283},
     year = {2020},
     volume = {25},
     number = {131},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2020_25_131_a2/}
}
TY  - JOUR
AU  - V. P. Maksimov
TI  - To estimating linear functionals values over solutions of systems with aftereffect
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2020
SP  - 274
EP  - 283
VL  - 25
IS  - 131
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2020_25_131_a2/
LA  - ru
ID  - VTAMU_2020_25_131_a2
ER  - 
%0 Journal Article
%A V. P. Maksimov
%T To estimating linear functionals values over solutions of systems with aftereffect
%J Vestnik rossijskih universitetov. Matematika
%D 2020
%P 274-283
%V 25
%N 131
%U http://geodesic.mathdoc.fr/item/VTAMU_2020_25_131_a2/
%G ru
%F VTAMU_2020_25_131_a2
V. P. Maksimov. To estimating linear functionals values over solutions of systems with aftereffect. Vestnik rossijskih universitetov. Matematika, Tome 25 (2020) no. 131, pp. 274-283. http://geodesic.mathdoc.fr/item/VTAMU_2020_25_131_a2/

[1] N. V. Azbelev, L. F. Rakhmatullina, “Theory of linear abstract functional differential equations and applications”, Memoirs on Differential Equations and Mathematical Physics, 8 (1996), 1–102 | MR

[2] N. V. Azbelev, V. P. Maksimov and L. F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations, Nauka, Moscow, 1991 (In Russian) | MR

[3] N. V. Azbelev, V. P. Maksimov and L. F. Rakhmatullina, Elements of the Contemporary Theory of Functional Differential Equations. Methods and Applications, Institute of Computer-Assisted Studies, Moscow, 2002 (In Russian) | MR

[4] N. V. Azbelev, V. P. Maksimov and L. F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations: Methods and Applications, Hindawi Publishing Corporation, New York–Cairo, 2007 | MR | Zbl

[5] N. V. Azbelev, V. P. Maksimov, P. M. Simonov, “Funktsionalno-differentsialnye uravneniya i ikh prilozheniya”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2009, no. 1, 3–23 ; N. V. Azbelev, V. P. Maksimov, P. M. Simonov, “Functional differential equations and applications”, International Journal of Pure and Applied Mathematics, 69:2 (2011), 203–235 | MR | MR | Zbl

[6] A. A. Boichuk, Constructive Methods of Analysis of Boundary Value Problems, Naukova Dumka, Kyiv, 1990 (In Russian) | MR

[7] A. I. Bulgakov, V. P. Maksimov, “Funktsionalnye i funktsionalno-differentsialnye vklyucheniya s volterrovymi operatorami”, Differentsialnye uravneniya, 17:8 (1981), 1362–1374 | MR

[8] M. G. Krein, A. A. Nudelman, The Markov Moment Problem and Extremal Problems, American Mathematical Society, New York, 1977 | MR | Zbl

[9] V. P. Maksimov, “O formule Koshi dlya funktsionalno-differentsialnogo uravneniya”, Differentsialnye uravneniya, 13:4 (1977), 601–606 | MR | Zbl

[10] V. P. Maksimov, Questions of the General Theory of Functional Differential Equations, Perm State University, Perm, 2003 (In Russian)

[11] V. P. Maksimov, “Theory of functional differential equations and some problems in economic dynamics”, Proceedings of the Conference on Differential and Difference Equations and Applications, eds. R. Agarwal, K. Perera, 2006, 757–765 | MR | Zbl

[12] V. P. Maksimov, “Linear overdetermined boundary value problems in Hilbert space”, Boundary Value Problems, 140 (2014) | MR | Zbl

[13] V. P. Maksimov, “On unreachable values of boundary functionals for overdetermined boundary value problems with constraints”, International Workshop QUALITDE – 2018, International Workshop QUALITDE -2018 (Tbilisi State University, Tbilisi, December 1-3, 2018), Tbilisi State University, Tbilisi, 2018, 127–131

[14] V. P. Maksimov, A. N. Rumyantsev, “Boundary value problems and problems of pulse control in economic dynamics: constructive study”, Russian Mathematics (Izv.VUZ), 37:5 (1993), 48–62 | MR | Zbl

[15] V. P. Maksimov, “On the construction and estimates of the Cauchy matrix for systems with aftereffect”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 3, 2019, 153–162 (In Russian)