On the existence of solutions to nonlinear boundary value problems for non-flat isotropic shells of Timoshenko type 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 non-flat 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.