On Resolving Boundary Value Problems of Nonlinear Theory for Timoshenko Types Shallow Shells

The article is devoted to proving the existence of solutions of geometrically nonlinear boundary value problem for Timoshenko type shallow shells which take into account the deformations of cross displacements. Equilibrium equations are reduced to a system of nonlinear singular integral equations on flat region, the resolution of which is established with the help of compressed reflections principle.