On the Problem of Solvability of Nonlinear Boundary Value Problems for Shallow Isotropic Shells of Timoshenko Type in Isometric Coordinates

The solvability of a boundary value problem for a system of five nonlinear second-order partial differential equations under given nonlinear boundary conditions, which describes the equilibrium state of elastic flat inhomogeneous isotropic shells with loose edges in the framework of the Timoshenko shear model, referred to isometric coordinates, is studied. The boundary value problem is reduced to a nonlinear operator equation with respect to generalized displacements in a Sobolev space, with the solvability of this equation being established using the contraction mapping principle.