Geodesic
Inverse problem for Euler--Poisson--Darboux abstract differential equation
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, Tome 15 (2006), pp. 126-141.

Voir la notice de l'article provenant de la source Math-Net.Ru

For the nonhomogeneous Euler–Poisson–Darboux equation in a Banach space, we consider the problem of determination of a parameter on the right-hand side of the equation by the excessive final condition. This problem can be reduced to the inversion of some operator represented in a suitable form and related to the operator solving the Cauchy problem for the homogeneous Euler–Poisson–Darboux equation. As the final result, we show that the solvability of the problem considered depends on the distribution of zeroes of some analytic function. In addition, we give a simple sufficient condition ensuring the unique solvability of the problem. 
@article{CMFD_2006_15_a8,
     author = {A. V. Glushak and V. A. Popova},
     title = {Inverse problem for {Euler--Poisson--Darboux} abstract differential equation},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {126--141},
     publisher = {mathdoc},
     volume = {15},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2006_15_a8/}
}
TY  - JOUR
AU  - A. V. Glushak
AU  - V. A. Popova
TI  - Inverse problem for Euler--Poisson--Darboux abstract differential equation
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2006
SP  - 126
EP  - 141
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2006_15_a8/
LA  - ru
ID  - CMFD_2006_15_a8
ER  - 
%0 Journal Article
%A A. V. Glushak
%A V. A. Popova
%T Inverse problem for Euler--Poisson--Darboux abstract differential equation
%J Contemporary Mathematics. Fundamental Directions
%D 2006
%P 126-141
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2006_15_a8/
%G ru
%F CMFD_2006_15_a8
A. V. Glushak; V. A. Popova. Inverse problem for Euler--Poisson--Darboux abstract differential equation. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, Tome 15 (2006), pp. 126-141. http://geodesic.mathdoc.fr/item/CMFD_2006_15_a8/

[1] Beitmen G., Erdeii A., Tablitsa integralnykh preobrazovanii, T. 2, Nauka, M., 1970

[2] Vasilev V. V., Krein S. G., Piskarev S. I., “Polugruppy operatorov, kosinus operator-funktsii i lineinye differentsialnye uravneniya”, Itogi nauki i tekhn. Ser. matem. analiz, 28, VINITI, M., 1990, 87–202 | MR

[3] Vatson G. N., Teoriya besselevykh funktsii, T. 1, IL, M., 1949

[4] Glushak A. V., “O vozmuschenii abstraktnogo uravneniya Eilera–Puassona–Darbu”, Matem. zametki, 60:3 (1996), 363–369 | MR | Zbl

[5] Glushak A. V., “Operatornaya funktsiya Besselya”, Dokl. RAN, 352:5 (1997), 587–589 | MR | Zbl

[6] Glushak A. V., Kononenko V. I., Shmulevich S. D., “Ob odnoi singulyarnoi abstraktnoi zadache Koshi”, Izvestiya vuzov. Matematika, 1986, no. 6, 55–56 | MR | Zbl

[7] Glushak A. V., Popova V. A., “Zadacha opredeleniya parametra abstraktnogo differentsialnogo uravneniya vysokogo poryadka”, Trudy matematicheskogo fakulteta VGU, no. 5, Voronezh, 2001, 42–52 | MR

[8] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Elementarnye funktsii, T. 1, Nauka, M., 1981 | MR | Zbl

[9] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Spetsialnye funktsii, T. 2, Nauka, M., 1983 | MR | Zbl

[10] Tikhonov I. V., Eidelman Yu. S., “Obratnaya zadacha dlya differentsialnogo uravneniya v banakhovom prostranstve i raspredelenie nulei tseloi funktsii tipa Mittag-Lefflera”, Diff. uravn., 38:5 (2002), 637–644 | MR | Zbl

[11] Khille E., Fillips R. S., Funktsionalnyi analiz i polugruppy, IL, M., 1962

[12] Khondo V. A., Voprosy vozmuscheniya abstraktnogo uravneniya Eilera–Puassona–Darbu, Deponirovano v VINITI, No 1971–1399, Voronezh, 1999

[13] Khondo V. A., “Zadacha opredeleniya parametra abstraktnogo uravneniya Eilera–Puassona–Darbu s ogranichennym operatorom”, Sbornik statei aspirantov i studentov matematicheskogo fakulteta VGU, Voronezh, 2000, 59–64