Upper and lower solution method for control of second-order Kolmogorov type systems
DOI:
https://doi.org/10.33993/jnaat541-1515Keywords:
Kolmogorov system, control problem, approximation algorithmAbstract
In this paper, an upper and lower solution method for the control of second-order Kolmogorov systems is introduced. Two iterative algorithms, one exact and one approximate, are proposed and their convergence is studied. The technique is based on Perov's fixed point theorem, matrices convergent to zero, and the use of Bielecki's norm.
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J. M. Coron, Control and Nonlinearity, Mathematical Surveys and Monographs, Vol. 136, Amer. Math. Soc., Providence, 2007.
A. Hofman and R. Precup, Vector fixed point approach to control of Kolmogorov diferential systems, Commun.Contemp. Math., 5 (2024) 1968-1981. DOI: https://doi.org/10.37256/cm.5220242840
A. Hofman and R. Precup, Control problems for Kolmogorov type second order equations and systems, submitted.
A. N. Kolmogorov, Sulla teoria di Volterra della lotta per l'esistenza, Giornale dell Istituto Italiano degli Attuari 7 (1936) 74-80.
J. D. Murray, An Introduction to Mathematical Biology, Vol. 1, Springer, New York, 2011.
L. G. Parajdi, R. Precup and I. S. Haplea, A method of lower and upper solutions for control problems and application to a model of bone marrow transplantion, Inter. J. Appl. Math. Comput. Sci. 33(3) (2023) 409-418. DOI: https://doi.org/10.34768/amcs-2023-0029
R. Precup, On some applications of the controllability principle for fixed point equations, Results Appl. Math. 13 (2022) 100236. DOI: https://doi.org/10.1016/j.rinam.2021.100236
R. Precup, Methods in Nonlinear Integral Equations, Springer, 2002. DOI: https://doi.org/10.1007/978-94-015-9986-3
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Copyright (c) 2025 Alexandru Hofman
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