Geodesic
On a nonlocal boundary value problem for the equation fourth-order in partial derivatives
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 37 (2021) no. 4, pp. 16-23

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In this article, we study a nonlocal problem for a fourth-order equation in which the existence and uniqueness of a solution to this problem is proved. The solution is constructed explicitly in the form of a Fourier series; the absolute and uniform convergence of the obtained series and the possibility of term-by-term differentiation of the solution with respect to all variables are substantiated. A criterion for the unique solvability of the stated boundary value problem is established.
Keywords: boundary value problem, Fourier method, existence and uniqueness of the solution. 
@article{VKAM_2021_37_4_a1,
     author = {O. Sh. Kilichov},
     title = {On a nonlocal boundary value problem for the equation fourth-order in partial derivatives},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {16--23},
     publisher = {mathdoc},
     volume = {37},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2021_37_4_a1/}
}
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O. Sh. Kilichov. On a nonlocal boundary value problem for the equation fourth-order in partial derivatives. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 37 (2021) no. 4, pp. 16-23. http://geodesic.mathdoc.fr/item/VKAM_2021_37_4_a1/