Geodesic
On the sing of the Green's function of the boundary value problem for the fourth-order equation on a graph
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 4, pp. 19-29 
R. Ch. Kulaev. On the sing of the Green's function of the boundary value problem for the fourth-order equation on a graph. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 4, pp. 19-29. http://geodesic.mathdoc.fr/item/VMJ_2013_15_4_a3/
@article{VMJ_2013_15_4_a3,
     author = {R. Ch. Kulaev},
     title = {On the sing of the {Green's} function of the boundary value problem for the fourth-order equation on a~graph},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {19--29},
     year = {2013},
     volume = {15},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2013_15_4_a3/}
}
TY  - JOUR
AU  - R. Ch. Kulaev
TI  - On the sing of the Green's function of the boundary value problem for the fourth-order equation on a graph
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2013
SP  - 19
EP  - 29
VL  - 15
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMJ_2013_15_4_a3/
LA  - ru
ID  - VMJ_2013_15_4_a3
ER  - 
%0 Journal Article
%A R. Ch. Kulaev
%T On the sing of the Green's function of the boundary value problem for the fourth-order equation on a graph
%J Vladikavkazskij matematičeskij žurnal
%D 2013
%P 19-29
%V 15
%N 4
%U http://geodesic.mathdoc.fr/item/VMJ_2013_15_4_a3/
%G ru
%F VMJ_2013_15_4_a3

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

In this paper we consider a boundary value problem for a fourth-order equation on a graph modeling the elastic deformation of the flat system of beams with the rigid connection conditions at the nodes. Some properties of the Green's function are investigated and a sufficient condition for its positivity is established.

[1] Pokornyi Yu. V., Bakhtina Zh. I., Zvereva M. B., Shabrov S. A., Ostsillyatsionnyi metod Shturma v spektralnykh zadachakh, Fizmatlit, M., 2009, 192 pp. | Zbl

[2] Pokornyi Yu. V., Penkin O. M., Pryadiev V. L., Borovskikh A. V., Lazarev K. P., Shabrov S. A., Differentsialnye uravneniya na geometricheskikh grafakh, Fizmatlit, M., 2004, 272 pp. | MR | Zbl

[3] Dekoninck B., Nicase S., “The eigenvalue problem for network of beams”, Generalized Functions, Operator Theory and Dimnamical Systems, Chapman and Hall Research in Math., 1999, 335–344 | MR | Zbl

[4] Dekoninck B., Nicase S., “Control of network of Euler–Bernoulli beams”, ESAIM: Control Optimisation and Calculus of Variations, 4 (1999), 57–82 | DOI | MR

[5] Lagnese J. E., Leugering G., Schmidt E. J. P. G., “Control of planar networks of Timoshenko beams”, SIAM J. Control Optim., 31 (1993), 780–811 | DOI | MR | Zbl

[6] Xu G. Q., Mastorakis N., “Stability of a star-shaped coupled network of strings and beams”, 10th WSEAS Int. Conf. on Math. Methods and Computational Techniques in Electrical Engineering, 2008, 148–154 | MR

[7] Borovskikh A. V., Mustafakulov R. O., Lazarev K. P., Pokornyi Yu. V., “Ob odnom klasse differentsialnykh uravnenii chetvertogo poryadka na prostranstvennoi seti”, Dokl. RAN, 345:6 (1995), 730–732 | MR | Zbl

[8] Pokornyi Yu. V., Mustafakulov R. O., “O pozitivnoi obratimosti nekotorykh kraevykh zadach dlya uravneniya chetvertogo poryadka”, Dif. uravneniya, 33:10 (1997), 1358–1365 | MR | Zbl

[9] Pokornyi Yu. V., Mustafakulov R. O., “O polozhitelnosti funktsii Grina lineinykh kraevykh zadach dlya uravnenii chetvertogo poryadka na grafe”, Izv. vuzov. Matematika, 1999, no. 2(441), 75–82 | MR | Zbl

[10] Zavgorodnii M. G., Maiorova C. P., “Ob odnom uravnenii matematicheskoi fiziki chetvertogo poryadka na grafe”, Issledovaniya po differents. uravneniyam i mat. modelirovaniyu, VNTs RAN i RSO-A, Vladikavkaz, 2008, 88–102

[11] Kulaev R. Ch., “O funktsii Grina kraevoi zadachi na grafe-puchke”, Izv. vuzov. Matematika, 2013, no. 2, 56–66 | Zbl

[12] Zavgorodnii M. G., “Variatsionnye printsipy postroeniya modelei sterzhnevykh sterzhnei”, Mat. modelir. informatsionnykh i tekhnologicheskikh sistem, 4, Voronezh. gos. tekhnol. akademiya, Voronezh, 2000, 59–62

[13] Pokornyi Yu. V., Penkin O. M., “O teoremakh sravneniya dlya uravnenii na grafakh”, Dif. uravneniya, 25:7 (1989), 1141–1150 | MR

[14] Pokornyi Yu. V., Karelina I. G., “O funktsii Grina zadachi Dirikhle na grafe”, Dokl. AN SSSR, 318:3 (1991), 942–944 | MR