SOLVABILITY OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR DIFFERENTIAL EQUILIBRIUM EQUATIONS OF NON-FLAT TIMOSHENKO TYPE SHELLS OF NON-ZERO GAUSSIAN CURVATURE 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 non-flat inhomogeneous isotropic shells with loose edges in the framework of the Timoshenko shear model, referred to isometric coordinates.The boundary value problem is reduced to a nonlinear operator equation with respect to generalized displacements in Sobolev space, the solvability of which is established using the principle of compressed mappings.