Geodesic
On existence of solutions to spatial nonlinear boundary-value problems for arbitrary elastic inhomogneous anisotropoic body
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 76-85

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We study the solvability of a nonlinear boundary-value problem for systems of nonlinear partial differential equations of second order. The aim of the work is the proof the theorem existence for solutions. The problem is reduced to a system of three-dimensional nonlinear singular integral equations, whose solvability can be proved with the use of the symbol of a singular operator and the principle of compressed mappings.
Keywords: elastic inhomogeneous anisotropic body, equilibrium equations, boundary-value problem, three-dimensional singular integral equations, symbol singular operator, existence theorem. 
@article{IVM_2019_1_a7,
     author = {S. N. Timergaliev and R. S. Yakushev},
     title = {On existence of solutions to spatial nonlinear boundary-value problems for arbitrary elastic inhomogneous anisotropoic body},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--85},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_1_a7/}
}
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S. N. Timergaliev; R. S. Yakushev. On existence of solutions to spatial nonlinear boundary-value problems for arbitrary elastic inhomogneous anisotropoic body. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 76-85. http://geodesic.mathdoc.fr/item/IVM_2019_1_a7/