Solvability of Some Systems of Integro-differential Equations in Population Dynamics Depending on the Natality and Mortality Rates

We establish the existence of stationary solutions for certain systems of reaction–diffusion-type equations in the corresponding H 2 spaces. Our method relies on the fixed point theorem when the elliptic problem contains second-order differential operators with and without the Fredholm property, whi...

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Bibliographic Details
Published inArnold mathematical journal Vol. 10; no. 1; pp. 1 - 22
Main Authors Vougalter, Vitali, Volpert, Vitaly
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2024
Subjects
Mathematics
Mathematics and Statistics
Research Contribution
35R09
35K91
35A01
35J91
Systems of integro-differential equations
Solvability conditions
Non-Fredholm operators
Stationary solutions
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Summary:We establish the existence of stationary solutions for certain systems of reaction–diffusion-type equations in the corresponding H 2 spaces. Our method relies on the fixed point theorem when the elliptic problem contains second-order differential operators with and without the Fredholm property, which may depend on the outcome of the competition between the natality and the mortality rates involved in the equations of the systems.
ISSN:2199-6792
2199-6806
DOI:10.1007/s40598-023-00225-6