Green's Functions and Spectral Theory for the Hill's Equation
Classical Analysis and ODEs
2015-11-04 v1
Abstract
The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann, Dirichlet, Mixed and anti-periodic problems as a combination of the Green's function related to periodic ones. As a consequence we will prove suitable results in spectral theory and deduce some comparison results for the solutions of the Hill's equation with different boundary value conditions.
Keywords
Cite
@article{arxiv.1511.00899,
title = {Green's Functions and Spectral Theory for the Hill's Equation},
author = {Alberto Cabada and José A. Cid and Lucía López Somoza},
journal= {arXiv preprint arXiv:1511.00899},
year = {2015}
}