We introduce the periodic and symmetric properties of the states in a class of weakly singular integral equations. The motivation of this study is due to the main results reported in a previous paper according to which bounded forces produce bounded states in the infinite field. We observe that within finite time, steady states develop. For each periodicity, two types of initial condition apply: the initial condition can be the same as the original condition, or be the steady state from the previous period. For symmetry, we apply forces of the same magnitude but in opposite directions.

integro-differential equation, weakly singular, periodicity, symmetry.

Received: October 16, 2023; Accepted: November 21, 2023; Published: December 29, 2023

How to cite this article: Shihchung Chiang, Periodicity and symmetry in a class of integral equations with weakly singular kernels, Far East Journal of Dynamical Systems 36(2) (2023), 153-164. http://dx.doi.org/10.17654/0972111823007

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] S. Chiang, Notes on the solution of a class of singular integral equations, Chung Hua Journal of Science and Engineering 3(4) (2005), 89-95.
[2] J. A. Burns, E. M. Cliff and T. L. Herdman, A state-space model for an aeroelastic system, Proceedings: 22nd IEEE Conference on Decision and Control 1983, pp. 1074-1077.
[3] S. Chiang, Numerical methods for solving a class of hybrid weakly singular integro-differential equations, Applied Mathematics (8) (2017), 956-966.
[4] S. Chiang and T. L. Herdman, On the infinite field of a class of weakly singular integral equations, Far East Journal of Dynamical Systems 34 (2022), 11-23.
[5] F. Kappel and K. P. Zhang, On neutral functional differential equations with nonatomic difference operator, J. of Math. Anal. and Application 113 (1986), 311-343.