Application of Special Function Spaces to the Study of Nonlinear Integral Equations Arising in Equilibrium Spatial Logistic Dynamics

Nikolaev, M. V., Dieckmann, U. ORCID: https://orcid.org/0000-0001-7089-0393, & Nikitin, A. A. (2021). Application of Special Function Spaces to the Study of Nonlinear Integral Equations Arising in Equilibrium Spatial Logistic Dynamics. Doklady Mathematics 104 (1) 188-192. 10.1134/S1064562421040128.

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Abstract

In this paper, we study a nonlinear integral equation that arises in a model of spatial logistic dynamics. The solvability of this equation is investigated by introducing special spaces of functions that are integrable up to a constant. Sufficient conditions for the biological characteristics and the parameters of the third spatial moment closure are established that guarantee the existence of the solution of the equation described above in some ball centered at zero. In addition, it is shown that this solution is unique in the considered ball and not zero. This means that, under appropriate conditions, the equilibrium state of the population of a certain species exists and does not coincide with the state of extinction.

Item Type: Article
Uncontrolled Keywords: functional analysis; mathematical biology; nonlinear integral equations
Research Programs: Advancing Systems Analysis (ASA)
Advancing Systems Analysis (ASA) > Cooperation and Transformative Governance (CAT)
Advancing Systems Analysis (ASA) > Exploratory Modeling of Human-natural Systems (EM)
Advancing Systems Analysis (ASA) > Systemic Rick and Resilience (SYRR)
Depositing User: Luke Kirwan
Date Deposited: 17 Nov 2021 14:28
Last Modified: 18 Nov 2021 14:26
URI: http://pure.iiasa.ac.at/17647

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