A Class of Problems in One-Dimensional Space

Abstract

In the present chapter we begin the study of a class of mathematical problems which, though relatively simple, may still be interpreted as non-linear problems of stability. These problems do not necessarily reflect any physical reality ; they represent mathematical models helpful in gaining understanding of certain non-linear phenomena. Moreover, from the mathematical point of view, the problems to be considered already contain certain difficulties which are typical of non-linear stability theory, so that their study can be considered as a first step in the construction of adequate methods of analysis for problems of greater complexity.