Anna Maria Candela (Università degli Studi di Bari Aldo Moro)
Genni Fragnelli (Università degli Studi di Siena)
Susana Gutierrez (University of Birmingham)
Dimitri Mugnai (Università degli Studi della Tuscia)
Shrish Parmeshwar (Univeristy of Bath)
Giusi Vaira (Università degli Studi di Bari Aldo Moro)
Abstracts:
Anna Maria Candela
Title: A new critical threshold for a family of quasilinear elliptic problems
Abstract: In the last years, by using variational arguments we have investigated the existence of solutions for a family of quasilinear elliptic problems, which generalize the classical p-Laplacian equation, with Dirichlet boundary conditions on bounded domains.
With respect to the classical p-Laplacian equation, they have a new critical threshold and we prove both a Pohŏzaev type nonexistence result on a star-shaped domain and an existence result.
Joint work with Kanishka Perera, Elisandra Gloss and Addolorata Salvatore.
Genni Fragnelli
Title: A new peridynamical operator
Abstract: In this talk, we introduce a new model for beam-type equations, driven by a mixed operator which is the sum of the classical biharmonic operator with a regional fractional Laplacian. The novelty is the peridynamical approach: the Dirichlet conditions hold in an extended outer domain (the horizon), which describes well the fact that a floor in reinforcedconcrete is stuck in the wall. We will present the spectral properties of this operator, studying stationary and evolution problems associated to it. Some open problems will be presented as well.
Susana Gutierrez
TBA
Dimitri Mugnai
Title: A magnetic Schr\"odinger-Poisson system with vanishing potentials
Abstract: We consider a magnetic Schrodinger-Poisson system in presence of potentials. In particular, we face the physical case in which the magnetic potential vanishes at infinity, showing some existence and multiplicity results for ground state solutions. We also treat the case of intertwining solutions, namely solutions which are invariant under the action of some finite or infinite groups.
Shrish Parmeshwar
Title: Solitonic Travelling Waves for the Gross-Pitaevskii Equation in a Strip
We discuss the Gross-Pitaevskii equation in the infinite strip Rx(0, 1), for positive width I>0, with Neumann boundary conditions. The one-dimensional equation on R admits a family of travelling wave solutions for wave speeds |c|<\sqrt{2}, S_{c}.
We show that for wave speeds c close enough to 0 and values of l close enough to some critical widths l_{c,k}, k\geq 1 an integer, there are travelling wave solutions \Psi_{l,k} that bifurcate from S_{c} and depend smoothly on the strip width l.
Giusi Vaira
Title: Blow-up phenomena for the Brezis-Nirenberg problem
Abstract: In this talk I will present some recent results regarding some open problem for a classical critical problem in a bounded domain in low dimensions. We will discuss the question of the existence of positive solutions and also non-existence that depends on the shape of the domain.