On the Existence of Solutions to Nonlinear Boundary Value Problems for Nonshallow Isotropic Timoshenko Shells in Arbitrary Curvilinear Coordinates

We study 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 nonshallow inhomogeneous isotropic shells with loose edges in the framework of the Timoshenko shear model, assigned to arbitrary curvilinear coordinates. The boundary value problem is reduced to a nonlinear operator equation for generalized displacements in Sobolev space, the solvability of which is established using the contraction mapping principle.