Method of Integral Equations for Studying the Solvability of Boundary Value Problems for the System of Nonlinear Differential Equations of the Theory of Timoshenko Type Shallow Inhomogeneous Shells

Abstract

The solvability of the boundary value problem for a system of second-order nonlinear partial differential equations with given boundary conditions which describes the equilibrium of elastic inhomogeneous shallow shells with free edges in the framework of the Timoshenko shear model is considered. The boundary value problem is reduced to a single nonlinear equation whose solvability is established by using the contraction mapping principle.