Palestra 1: 

Título:  Elliptic systems with vanishing weights

Palestrante: Juan Arratia - Universidad de Santiago de Chile - Chile 

Abstract.:      

We present two main results. First, we study a system with nonnegative vanishing potentials V1, V2 and nonlinearities involving vanishing weights, inspired by the Brezis-Kamin framework [2]. Using a monotonicity approach, we establish the existence of a bounded solution and, under certain conditions, a second solution for two specific cases: a gradient system and a Hamiltonian system.

Second, we extend the work of Ambrosetti, Cerami, and Ruiz [1] by analyzing nonlinearities that involve vanishing weights and sublinear growth. We establish precise conditions on the powers and parameters that guarantee the existence and uniqueness of positive bounded solutions.

Palestra 2:

Título:  Some results about nonlinear equations on graph

Palestrante: Jiazheng Zhou - Universidade de Brasilia

Abstract.:      

This work, we present some results about nonlinear equations on graph: 1. existence and multiplicity of positive solutions to nonlinar Schrodinger equations on a bridge type unbounded graph; 2. stability of constant steady states in Reaction-Diffusion systems on graphs.