Solvability of Nonlinear Boundary Value Problems for Differential Equilibrium Equations of Nonflat Timoshenko Type Shells of Nonzero Gaussian Curvature in Isometric Coordinates

We study the solvability of a boundary value problem for a system of five nonlinearsecond-order partial differential equations under given nonlinear boundary conditions, whichdescribes the equilibrium state of elastic nonshallow inhomogeneous isotropic shells with free edgesin the framen of the Timoshenko shear model in isometric coordinates. The boundary valueproblem is reduced to a nonlinear operator equation for the generalized displacements in a Sobolevspace, the solvability of which is established using the contraction mapping principle.