Spectral Analysis of Banach Spaces and their Application to Age-Structured Equations. Cambodia Journal of Basic and Applied Research (CJBAR), 3(2),

Abstract

In this paper, Floquet's theory will be applied to a positive periodic operator on a Banach space to show the existence and uniqueness of a solution to Floquet eigenvalue problems and their adjoints. Then, the theory will be applied to an age-structured equation with positive and periodic coefficients to study a Floquet exponent, which measures the growth rate of a population. At the same time, exponential and long- run asymptotic decay will be derived using the entropy method.