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, which may depend on the outcome of the competition between the natality and the mortality rates involved in the equations of the systems.