Proof of the solvability of a system of partial differential equations in the nonlinear theory of shallow shells of Timoshenko type

Abstract

We study the solvability of a system of second-order partial differential equations under given boundary conditions. To prove the existence of a solution of the system, we reduce it to a single nonlinear partial differential equation whose solvability is proved with the use of the contraction mapping principle. © 2012 Pleiades Publishing, Ltd.