Monotonicity of a Class of Integral Functionals

TL;DR

This paper establishes a monotonicity condition for a class of integral functionals involving functions of bounded variation and applies it to analyze a structured population model.

Contribution

It introduces a new monotonicity condition for integral functionals and demonstrates its application to structured population dynamics.

Findings

Monotonicity condition for integral functionals proved

Application to structured population model analyzed

Insights into population behavior derived from the functional analysis

Abstract

In this note we prove a condition of monotonicity for the integral functional $ F(g) = \int_a^b h(x)\, d[-g(x)] $ with respect to $g$, a function of bounded variation. This condition is applied to analyze the behavior of a generalized structured population model.