Abstract
The aim of this paper is to draw attention to a general principle for solving control problems for operator equations with the help of fixed point techniques. Three distinct applications are presented: a control problem related to the Lotka–Volterra system, the nonlinear Stokes system, and radial solutions of the Neumann problem for φ-Laplace equations. Only for the first application, the control is an explicit external one, while for the next two applications, the control is dependent on the models and arises from the necessity to conform to the actual modeled process or to a certain boundary condition. From the perspective of those interested in applications, the three examples of problems of such a different nature, we believe have been able to suggest the wide applicability of our method thus paving the way for new applications. From a theoretical perspective, the method leading to fixed point equations with composed operators is suitable to be related to advanced research in fixed point theory for single-valued and multi-valued operators.
Authors
Radu Precup
Institute of Advanced Studies in Science and Technology, Babes-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
Keywords
Paper coordinates
R. Precup, On some applications of the controllability principle for fixed point equations, Results Appl. Math., 13 (2022), art. no. 100236, https://doi.org/10.1016/j.rinam.2021.100236
About this paper
Journal
Results in Applied Mathematics
Publisher Name
Elsevier
Print ISSN
Online ISSN
25900374
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