New trends in periodic problems and determining related eigenvalues

In this chapter, we address the aforementioned issues one by one. We start by formulating periodic BVPs and, then, introduce a pFMNI and a contour -integral -based eigenvalue-solver called the Sakurai -Sugiura method (SSM). We discuss techniques related to the analytic continuation of tools for pFMNI to complex frequencies, as well as a simple method of making distinction between true and fictitious eigenvalues. We finally consider numerical examples, followed by conclusions. More information on the theoretical developments related to the content of this chapter can be found.