A Survey of the Theory of the Boundedness, Stability, and Asymptotic Behavior of Solutions of Linear and Non-Linear Differential and Difference Equations

Abstract

Abstract : The nature of solutions of differential and difference equations is of great interest to the applied mathematician, the physicist, and the engineer. In particular, numerous problems of vital concern to the Navy in connection with the self-excitation of oscillations in electronic and mechanical systems, the stability of moving bodies, the steering and turning of ships, etc. lead to non-linear differential equations. Thus far, results in the theory of these equations have been comparatively disorganized, and this survey should be useful in the unification and further development of the field. The Office of Naval Research is therefore pleased to make this report available in accordance with its statutory function of disseminating scientific information.