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

• Published in: Arnold mathematical journal Vol. 10; no. 1; pp. 1 - 22
• Main Authors: Vougalter, Vitali, Volpert, Vitaly
• Format: Journal Article
• Language: English
• 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

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...