A fixed-point approach to control problems for Kolmogorov type second-order equations and systems

Abstract

In this paper, the second-order differential equations and systems of Kolmogorov type are defined. With reference to population dynamics models, unlike the first-order equations which give the expression of the per capita rate, in the case of the second-order equations, the law of change of the per capita rate is given. Several control problems with fixed final time and fixed final state, with additive and multiplicative control, are studied. Their controllability is proved with fixed-point methods, the theorems of Banach, Schauder, Krasnoselskii, Avramescu and Perov.