Geodesic
The problem with shift for the Bitsadze--Lykov equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2012), pp. 26-36.

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

The Bitsadze-Lykov equation is considered. The problem with shift containing the Kober–Erdélyi and M. Saigo operators in boundary condition is set for this equation. The questions of uniqueness (ununiqueness) of this problem solution with different functions and constants in boundary condition are investigated. The number of theorems is formulated and proved.
Keywords: Bitsadze–Lykov equation, boundary value problem, Kober–Erdélyi operator, M. Saigo operator, Riemann–Liouville operator, existence and uniqueness of the problem solution. 
@article{VSGTU_2012_4_a2,
     author = {E. Yu. Arlanova},
     title = {The problem with shift for the {Bitsadze--Lykov} equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {26--36},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a2/}
}
TY  - JOUR
AU  - E. Yu. Arlanova
TI  - The problem with shift for the Bitsadze--Lykov equation
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2012
SP  - 26
EP  - 36
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a2/
LA  - ru
ID  - VSGTU_2012_4_a2
ER  - 
%0 Journal Article
%A E. Yu. Arlanova
%T The problem with shift for the Bitsadze--Lykov equation
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2012
%P 26-36
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a2/
%G ru
%F VSGTU_2012_4_a2
E. Yu. Arlanova. The problem with shift for the Bitsadze--Lykov equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2012), pp. 26-36. http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a2/

[1] Luikov A. V., “Application of the methods of thermodynamics of irreversible processes to the investigation of heat and mass transfer”, J. Eng. Physics Thermophysics, 9:3 (1965), 189–202 | DOI

[2] Bitsadze A. V., Equations of the Mixed Type, Pergamon Press, New York, 1964, xiii+160 pp. | MR | Zbl

[3] Nakhushev A. M., Equations of mathematical biology, Vyssh. Shk., Moscow, 1995, 301 pp. | Zbl

[4] Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives: Theory and Applications, Gordon Breach, New York, 1993, xxxvi+976 pp. | MR | MR | Zbl | Zbl

[5] Nakhushev A. M., Fractional calculus and its applications, Fizmatlit, Moscow, 2003, 271 pp. | Zbl

[6] Saigo M., “A certain boundary value problem for the Euler–Darboux equation”, Math. Japon, 24:4 (1979), 377–385 | MR | Zbl

[7] Zhegalov V. I., “A boundary-value problem for an equation of mixed type with boundary conditions on both characteristics and with discontinuities on the transition curve”, Boundary value problems in the theory of analytic functions, Kazan. Gos. Univ. Uchen. Zap., 122, no. 3, Kazan University, Kazan, 1962, 3–16 | MR | Zbl

[8] Nakhushev A. M., “A new boundary value problem for a degenerate hyperbolic equation”, Sov. Math., Dokl., 10 (1969), 935–938 | Zbl

[9] Nakhushev A. M., “On Some Boundary Value Problems for Hyperbolic Equations and Equations of the Mixed Type”, Differ. Uravn., 5:1 (1969), 44–59 | Zbl

[10] Nakhushev A. M., Problems with Shift for Partial Differential Equations, Nauka, Moscow, 2006, 287 pp.

[11] Repin O. A., Kumykova S. K., “A nonlocal problem for the Bitsadze-Lykov equation”, Russian Math. (Iz. VUZ), 54:3 (2010), 24–30 | DOI | MR | Zbl

[12] Bitsadze A. V., Some classes of partial differential equations, Nauka, Moscow, 1981, 448 pp. | MR

[13] Tricomi F., On linear partial differential equations of the second order of mixed type, Brown University, Dayton, 1948, 372 pp.

[14] Kilbas A. A., Integral equations. A course of lectures, BGU, Minsk, 2005, 143 pp. | Zbl

[15] Erdélyi A., Magnus W., Oberhettinger F., Tricomi F. G., Higher transcendental functions, v. I, ed. H. Bateman, McGraw-Hill Book Co, Inc., New York – Toronto – London, 1953, 302 pp. ; Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii. V 3-kh t, v. 1, Gipergeometricheskaya funktsiya. Funktsiya Lezhandra, Nauka, M., 1973, 296 pp. | Zbl

[16] Nakhushev A. M., “Inverse problems for degenerate equations and Volterra integral equations of the third kind”, Differ. Uravn, 10:1 (1974), 100–111 | Zbl