Solvability of Nonlinear Boundary Value Problemsfor Differential Equilibrium Equations of Nonflat Timoshenko Type Shells of Nonzero GaussianCurvature in Isometric 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 free edges in the framen of the Timoshenko shear model in isometric coordinates. The boundary value problem is reduced to a nonlinear operator equation for the generalized displacements in a Sobolev space, the solvability of which is established using the contraction mapping principle.