Among the various courses offered to the schools of the Friuli Venezia Giulia region by the University of Trieste, for the PNRR project ‘Active orientation in the school-university transition’, within the framework of the National Recovery and Resilience Plan, Mission 4 ‘Education and Research’ Investment 1.6, we proposed a didactic activity in mathematics related to the topic of social sustainability. In this contribution, we present a description of the activity carried out, with various ideas that can be used in the curriculum hours or in complementary activities. The topic presented concerns an introduction to discrete dynamical systems, with a focus on linear and exponential growths. The activity was proposed to several classes in the third, fourth and fifth year of high schools. Naturally, methods and topics were adapted according to the level of the students present. Topics considered more challenging or more advanced are marked with the symbol . The lectures were complemented by various group work and workshops, which we report only in part.

An existence result to some nonlinear Neumann elliptic problems defined on balls has been provided recently by the author in [21]. We investigate, in this paper, the possibility of extending such a result to annuli.