Spectral theory and Green's functions related to nonlocal differential equations. Application to nonlinear problems

Abstract

Differential equations represent an important tool for solving many real problems. In this thesis we focus on the qualitative properties of the solutions of functional equations with nonlocal boundary conditions, focusing on the study of constant sign solutions. We will study comparison results between the Green's functions related to the Hill's equation subject to different boundary conditions. The relationship between the respective spectra of the different problems considered will be also studied. Finally, we will addressed the study of nonlinear systems subject to nonlocal linear boundary conditions and the spectral charaterization of the constant sign derivatives of the Green's function.