8h20/ Prof. Claudianor Oliveira Alves
Title: Existence of Normalized Solution for Some Elliptic Problems in Bounded Domains
Abstract: In this talk, we will discuss the existence of solutions for various types of elliptic problems and present a recent result from a collaboration with Liejun Shen (China), where we address the existence of normalized solutions in bounded domains. A new approach to establishing the existence of such solutions will be presented.
9h10/Prof. Pammella Queiroz de Souza
Title: Stability of a Tree-Shaped Network of Timoshenko System
Abstract: In this talk, we will examine a tree-shaped network R consisting of three edges of Timoshenko beams, connected at a single vertex. We assume that the root of the network is clamped, the displacements at the interior node are continuous, and the forces satisfy the transmission conditions. Furthermore, we assume that no control is applied to the first edge (i=1), while internal local controls are applied to the other two edges (i=2,3). Under these conditions, we will address the stabilization problem and demonstrate that the closed-loop system is exponentially stable. Finally, we will discuss the generalization of this result to a network with N+1 edges. I will present the results in collaboration with Julie Valein from Université de Lorraine and Mohammad Akil from Université Polytechnique Hauts-de-France.
09h50/Coffe Break
10h10/Prof. Marco Aurélio Soares Souto
Title:A Sufficient Condition to Bound Cerami Sequences for Euler-Lagrange Functionals of Superlinear Elliptic Problems in Bounded Domains
Abstract: We will present a condition on the nonlinearity that is weaker than Ambrosetti-Rabinowitz and others, to obtain the boundedness of Cerami sequences in bounded domains.
11h00/Prof. Alânnio Barbosa Nobrega
Title: An Ambrosetti-Prodi Problem for the Finsler $p$-Laplacian
Abstract: In this talk, we will discuss the Finsler $p$-Laplacian operator and present some results on the existence and multiplicity of solutions that we have been studying, including an Ambrosetti-Prodi type result.
11h40/Prof. Denilson da Silva Pereira
Title: Semilinear elliptic problems involving a fast increasing diffusion weight
Abstract: In this talk we present recent results involving elliptic problems with sublinear growth at the origin and superlinear behavior at infinity with bounded weights in $\mathbb{R}^n$. Problems of this nature present several difficulties to deal with variationally, once that the energy functional is not, a priori, well defined. We overcome this difficulty by obtaining a first solution, via the sub and super solution technique. Understanding the behavior at infinity of this first solution, we are able to obtain a second solution via variational methods.
Joint work with Pedro Ubilla (USACH), Juan Arratia(USACH) and Diego Ferraz (UFRN).
