Geodesic
On the problem of solvability of nonlinear boundary value problems for shallow isotropic shells of Timoshenko type in isometric coordinates
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2024), pp. 50-68 Cet article a éte moissonné depuis la source Math-Net.Ru

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The solvability of a boundary value problem for a system, which describes the equilibrium state of elastic shallow inhomogeneous isotropic shells with loose edges referred to isometric coordinates in the Timoshenko shear model and consists of five non-linear second-order partial differential equations under given non-linear boundary conditions, is studied. The boundary value problem is reduced to a nonlinear operator equation for generalized displacements in Sobolev space, the solvability of this equation is established with the help of the contraction mapping principle.
Keywords: shallow isotropic inhomogeneous shell of Timoshenko type, isometric coordinates, nonlinear boundary value problem, generalized solution, integral representation, holomorphic function, operator equation, existence theorem. 
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S. N. Timergaliev. On the problem of solvability of nonlinear boundary value problems for shallow isotropic shells of Timoshenko type in isometric coordinates. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2024), pp. 50-68. http://geodesic.mathdoc.fr/item/IVM_2024_1_a3/

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