LAUSR

We study the solvability of a nonlinear boundary value problem for a system of five second-order partial differential equations under given boundary conditions. The system describes the equilibrium state of elastic shallow inhomogeneous anisotropic shells with free edges in the framework of the Timoshenko shear model. The boundary value problem is reduced to a nonlinear operator equation for generalized displacements in a Sobolev space, whose solvability is established with the use of the contraction mapping principle.