Qualitative Behavior of the Solutions to Delay and Difference Euations (Вестник КазНУ. Серия математика, механика, информатика, 2018)
It is noteworthy to observe that a first-order linear ordinary differential equation without delaydoes not possess oscillatory solutions. Therefore the investigation of oscillatory solutions is ofinterest for equations with delays or for the discrete analogue difference equations. Furthermore, themathematical modelling of several real-world problems leads to differential equations that dependon the past history rather than only the current state. In this article conditions are presentedsuch that all solutions of delay and difference equations are oscillatory while all solutions of thecorresponding ordinary differential equations without delay are, for example, decreasing and tendto zero. Equations with constant and variable arguments are investigated. Several examples ofdelay and difference equations with applications to many sectors of life are presented.
Keywords: oscillation; delay differential equations; difference equations