Lecturer:
Guglielmo Feltrin (University of Udine)

Board Contact:
Guglielmo Feltrin

The course aims primarily to introduce a range of topological tools that are useful for addressing nonlinear problems in mathematical analysis, with particular emphasis on ordinary differential equations and complex dynamical phenomena such as bifurcation, resonance, and chaos. Unlike purely analytical methods, topological methods make it possible to prove the existence and multiplicity of solutions and to investigate their qualitative properties, even in the absence of explicit formulas. These methods are robust and often applicable in very general settings.

Throughout the course, we will explore various techniques, both classical - such as the method of upper and lower solutions - and more modern ones, such as the stretching-along-the-paths method, through simple illustrative examples. We will also discuss the use of these techniques in recent research for the analysis of real-world models.