Geodesic
On a boundary value problem for a high order mixed type equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 899-912

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In this paper, we study a Dirichlet type problem for a Lavrentiev–Bitsadze type equation of high order type in a rectangular domain. The necessary and sufficient conditions for the uniqueness of the problem solution are obtained by using the spectral method. The solution is constructed in the form of a series of eigenfunctions. When substantiating the convergence of a series, the problem of «small» denominators arises. Sufficient conditions are obtained for the separability of the «small» denominator from zero.
Keywords: Differential equation, mixed type, boundary value problem, eigenvalue, eigenfunction, determinant, uniqueness, «small» denominators, series
Mots-clés : existence, convergence. 
@article{SEMR_2020_17_a94,
     author = {B. Yu. Irgashev},
     title = {On a boundary value problem for a high order mixed type equation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {899--912},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a94/}
}
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B. Yu. Irgashev. On a boundary value problem for a high order mixed type equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 899-912. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a94/