On existence of solutions to spatial nonlinear boundary-value problems for arbitrary elastic inhomogneous anisotropoic body

S. N. Timergaliev^a, R. S. Yakushev<sup>b

a</sup> Kazan State Achitecture and Civil Engineering University, 1 Zelyonaya str., Kazan, 420043 Russia
^b Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: 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.

UDC: 517.958:539.3

Received: 02.11.2017
Revised: 02.11.2017
Accepted: 22.03.2018

DOI: 10.26907/0021-3446-2019-1-76-85

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:1, 67–75

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