A fixed-point approach to control problems for Kolmogorov type second-order equations and systems

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(original), Fixed point theory, ISI/JCR, Mathematical modeling, models in biomathematics, Nonlinear analysis, ODEs (theory), paper

Abstract

In this paper, the second-order differential equations and systems of Kolmogorov type are defined. With reference to population dynamics models, unlike the first-order equations which give the expression of the per capita rate, in the case of the second-order equations, the law of change of the per capita rate is given. Several control problems with fixed final time and fixed final state, with additive and multiplicative control, are studied. Their controllability is proved with fixed-point methods, the theorems of Banach, Schauder, Krasnoselskii, Avramescu and Perov.

Authors

Radu Precup
Faculty of Mathematics and Computer Science and Institute of Advanced Studies in Science and Technology Babes-Bolyai University, Cluj-Napoca Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania

Alexandru Hofman
Faculty of Mathematics and Computer Science Babes-Bolyai University, Cluj-Napoca Romania

Keywords

Kolmogorov system; Lotka–Volterra system; control problem; fixed point; matrix convergent to zero; Volterra–Fredholm integral equation.

Paper coordinates

Al. Hofman, R. Precup, A fixed-point approach to control problems for Kolmogorov type second-order equations and systems, 27 (2025), art. no. 7, https://doi.org/10.1007/s11784-024-01160-5

PDF

freely available at the publisher

About this paper

Journal

Journal of Fixed Point Theory and Applications

Publisher Name

Springer Nature

DOI

https://doi.org/10.1007/s11784-024-01160-5

Print ISSN

1661-7738

Online ISSN

1661-7746

google scholar link

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