This book presents rigorous treatment of boundary value problems in nonlinear theory of shallow shells. The consideration of the problems is carried out using methods of nonlinear functional analysis.
The Main Boundary Value Problems in the Nonlinear Theory of Shallow Shells.- General Mathematical Questions.- Topological Methods Applied to Solvability of the Main Boundary Value Problems of the Nonlinear Theory of Shallow Sells in Displacements.- The Tolopological Method in the Problem of Solvability of the Main Boundary Value Problems in the Nonlinear Theory of Shallow Shells with an Airy Stress Function.- The Variational Approach to the Problem of Solvability of Boundary Value Problems of Nonlinear Shallow Shell Theory.- Numerical-Analytical Methods in the Nonlinear Theory of Shallow Shells.- Direct Methods in the Nonlinear Theory of Shallow Shells.- Formulation of the Problem of Stability. Global Uniqueness of Solutions. Stiffness of Shells. Well-Posedness Classes.- Stability in the Large of the Membrane State of a Shallow Shell. Existence of the Lower Critical Value.- A Probabilistic Approach to the Problem of Stability of Shallow Shells.
