Floquet Bloch Theory Used to Analyze the Stability of Periodic Systems

Abstract

This study, the role and effects of Floquet Bloch theory on partial differential equations with periodic coefficients were investigated. Results are given about the Floquet expansions of arbitrary solutions, the solvability of non-homogeneous equations, the existence and structure of solutions, especially for boundary value problems that arise in applications of Schrödinger equations. This theory is of great importance for the quantum theory of solids, the theory of waveguides, scattering theory and other fields of mathematical and theoretical physics.