Equations with Periodic Coefficients

Abstract

In this chapter we discuss differential equations whose coefficients are periodic and the properties of their solutions. Such equations appear in various fields of science, e.g., solid state physics, celestial mechanics and others. Our objective is then to investiage the implications of periodicity on these systems properties and behavior. From another point of view, many physical systems are invariant with respect to certain transformations of the independent and dependent variables. Accordingly, the corresponding differential equations which model these systems are invariant under the same transformations. However, surprisingly not all solutions to these equations are invariant with respect to these same transformations. We shall illustrate this phenomena (and its partial resolution) within the context of periodic equations.