Floquet theory for integral and integro-differential equations
S. A. Belbas
TL;DR
This paper extends Floquet theory and Hill's method to analyze the stability of integral and integro-differential equations with periodic coefficients, providing new analytical tools for stability boundary determination.
Contribution
It develops an analytical extension of Hill's method for integro-differential equations, offering insights into stability boundaries and qualitative properties.
Findings
Extended Hill's method to integro-differential equations
Derived stability boundary criteria
Provided qualitative stability properties
Abstract
We study the extension of Hill's method of infinite determinants to the case of integro-differential equations with periodic coefficients and kernels. We develop the analytical theory of such methods, and we obtain certain qualitative properties of the equations that determine the boundaries between regions of dynamic stability and dynamic instability.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Differential Equations and Numerical Methods · Stability and Controllability of Differential Equations