Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022)

Mixed differential equations with advance and delay occur in many problems in economy, biology, physics and engineering. The concept of delay is related to the memory of systems, where past events influence current behavior. The concept of advance is related to potential future events which are known at the current time, and which could be useful for decision making. In this article various examples are given of difference and differential equations, classical, with delay, and with delay and advances (the mixed ones). It is well known that the solutions of these types of equations cannot be obtained in closed form. It is not quite clear how to formulate an initial value problem for such equations and the existence and uniqueness of solutions becomes a complicated issue. To study the oscillation of solutions of differential equations, we need to assume that there exists a solution of such equations on the half line.