Geodesic
Mixed problem for an integro-differential equation with a multidimensional pseudoparabolic operator and nonlinear deviation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations, geometry, and topology, Tome 201 (2021), pp. 33-43

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In this paper, we examine the unique generalized solvability and construct a solution to a nonlinear multidimensional mixed problem for a fourth-order nonlinear pseudoparabolic integro-differential equation with a degenerate kernel and nonlinear deviation. We establish sufficient coefficient conditions for the unique solvability of the nonlocal problem for regular values of the spectral parameter. The research is based on the Fourier method of separation of variables, the method of successive approximations, and the method of contraction mappings.
Keywords: multidimensional mixed problem, integro-differential equation, degenerate kernel, nonlinear deviation, generalized solvability. 
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     author = {T. K. Yuldashev (Iuldashev) and F. D. Rakhmonov},
     title = {Mixed problem for an integro-differential equation with a multidimensional pseudoparabolic operator and nonlinear deviation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {33--43},
     publisher = {mathdoc},
     volume = {201},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_201_a2/}
}
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T. K. Yuldashev (Iuldashev); F. D. Rakhmonov. Mixed problem for an integro-differential equation with a multidimensional pseudoparabolic operator and nonlinear deviation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations, geometry, and topology, Tome 201 (2021), pp. 33-43. http://geodesic.mathdoc.fr/item/INTO_2021_201_a2/