Monotone Methods in Mathematics

In a large number of mathematical problems, we are interested in determining if they have a solution and if such
the solution is unique, as well as in its properties, such as positivity, boundedness, and asymptotic behavior among others. Monotone methods generate, from linear iterative processes, monotone sequences that converge to the solution of nonlinear problems, among these are ordinary, partial, stochastic, and delayed differential equations. In this talk, we will learn what we need to implement a monotone method and how they allow us to answer each of the aforementioned concerns.