New Directions of Research in the Theory of Differential Equations

Abstract

Publisher Summary This chapter focuses on the new directions of research in the theory of differential equations. The new directions of research in the theory of differential equations indicates its applications in a number of recent scientific and technological developments such as the theory of control processes, the study of time lags, hereditary processes and nonlocal physical theories, nuclear reactors and planetary atmospheres, and digital computers. Each advance permits to survey both the modern and the classic in a new light and reveals novel and unsuspected interconnections and simplifications. The invariant imbedding offers a way of treating variational problems as initial value problems despite the fact that the usual procedure yields a differential equation with two-point boundary conditions. This approach introduces initial value equations and provides a systematic means of establishing the existence and uniqueness of solutions of many equations, which classical techniques do not handle easily.