Geodesic
Boundary value problem for an inhomogeneous fourth order equations with constant coefficients
Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 2, pp. 157-172

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For a fourth-order equation with constant coefficients, a boundary value problem in a rectangular domain is considered. The uniqueness of a solution of the stated problem is proved by the method of energy integrals. The solution is written in terms of the constructed Green's function. In substantiating the uniform convergence, the “small denominator” is established to be nonzero.
Keywords: fourth-order equation, multiple characteristics, lower terms, boundary value problem, uniqueness of solution, existence of solution, Green's function. 
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     author = {Yu. P. Apakov and S. M. Mamajonov},
     title = {Boundary value problem for an inhomogeneous fourth order equations with constant coefficients},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
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     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_2_a0/}
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Yu. P. Apakov; S. M. Mamajonov. Boundary value problem for an inhomogeneous fourth order equations with constant coefficients. Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 2, pp. 157-172. http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_2_a0/