A dynamical approach to lower and upper solutions for planar systems. ``To the memory of Massimo Tarallo''
The theory of lower and upper solutions appears usually for some second order scalar ordinary differential equations with separated boundary conditions, which was developed in several directions, by different methods. In this paper, authors have proved the existence of bounded and periodic solutions for planar systems \[x'=f(t,x,y),\quad y'=g(t,x,y)\] by introducing a notion of lower and upper solutions, which generalizes the classical one on the existence of bounded, periodic for scalar second order equations. The new approach is based on a dynamical study of the solutions. Finally, they provide some corollaries on the existence of almost periodic solutions for scalar second order equations.
scientific article; zbMATH DE number 7356216
scientific article