Existence and uniqueness of positive periodic solutions of a certain functional differential equation

In our work, we prove the existence and uniqueness of positive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mn>1</mml:mn> </mml:math> -periodic solutions of a first order differential equation that contains a piecewise constant term. Such equations admit periodic solutions and hence they can be used for numerical modelling of temperature changes in a space surrounded by environment with different temperature. For some types of functional equations, it is possible to use the comparison principle method of differential equations to obtain existence, uniqueness, and asymptotic stability results.