Analysis/PDE’S seminar
Coordenador: Abiel Costa Macedo
Our Analysis/PDE’S seminar starts at 8.30 am and can be accessed by clicking on the date.
DATE  TALK 
06/08/2020  ABSTRACT In this talk, we shed new light on the classical inequality by G.H. Hardy 1920 and discuss some related extremal problems. We aim to connect it with existence results for a wide range of differential equations on radially symmetric domains, including kHessian operator for fully nonlinear regime k > 1, and either critical or supercritical growth nonlinearities for both exponential and pure powertype growths. Title: Hardytype inequality and kHessian equations Speaker: José Francisco de Oliveira(DMAT/UFPI) 
13/08/2020  ABSTRACT In the talk we consider a class of elliptic problems with a nonlinearity which is nonlocal and with homogeneous Dirichlet boundary condition. Moreover the nonlinearity can make the problem degenerate since it may even have multiple singularities in the nonlocal variable. We use fixed point arguments for an appropriately defined solution map, to produce multiplicity of classical positive solutions with ordered norms. Title: Positive solutions for a singular problem Speaker: Gaetano Siciliano(IME/USP) 
20/08/2020  ABSTRACT In the talk we deal with Hamiltonian elliptic systems in two dimensions and bounded domains, with one of the nonlinearities having exponential growth condition. We derive the maximal growth conditions allowed for the other one, proving that it can be of exponential type, doubleexponential type, or completely arbitrary, depending on the conditions required for the first one. Under these hypotheses, we prove existence of nontrivial solutions for the system. Title: Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions Speaker: Bruno Henrique Carvalho Ribeiro(DMAT/UFPB) 
27/08/2020  ABSTRACT In this talk, I'm going to present a variational approach for the M.S.P system using the concentrationcompactness principal presented by P.l.lions in his famous paper on this subject. Title: Existence of Steady States For The MaxwellSchrodingerPoisson System by The ConcentrationCompactness Principal. Speaker: Gabriel Neves Cunha(IME/UFG) 
03/09/2020  ABSTRACT In this talk, we deal with an autonomous nonLipschitz semilinear elliptic equation. We study the existence of a weak solution that satisfies some specific boundary conditions in some subset of the boundary, while in the rest of the boundary the Hopf maximum principle is violated, the socalled "free boundary solutions". In approaching this problem, the main techniques to the proof are the Pohozaev's type of identity and the generalized nonlinear Rayleigh quotients method. Title: On free boundary periodic solutions for equations with nonLipschitz nonlinearity Speaker: Fábio Sodré Rocha(IME/UFG) 
10/09/2020 
ABSTRACT Then, through a careful analysis of the fiber maps associated to the energy functional, we will prove existence, nonexistence and multiplicity of solutions of our problem when the parameters a, b, λ vary in appropriate intervals. When the nonlinearity g is a pure power term, i.e. g(x, u) = u^{p−2}u for some p ∈ (2, 2^{*}), through a detailed study of the Nehari sets associated to the problem, we will show the existence of two critical hyperbolas on the plane (a, b) that separates the plane into regions where the energy functional exhibits distinct topological properties.
Title: ON A CRITICAL KIRCHHOFF TYPE PROBLEM IN HIGH DIMENSION Speaker: Francesca Faraci(Department of Mathematics and Computer Sciences/ UNICT)

17/09/2020 
ABSTRACT 
24/09/2020  ABSTRACT In this talk, we review some wellknown results for the eigenvalues of the Dirichlet pLaplace operator. After, we study the existence of sequences of variational eigenvalues to nonlocal nonstandard growth problems ruled by the fractional gLaplacian operator with different boundary conditions (Dirichlet, Neumann and Robin). Due to the nonhomogeneous nature of the operator several drawbacks must be overcome, leading to some results that contrast with the case of power functions. The analysis developed in this talk extends the abstract framework corresponding to some standard cases associated with the pLaplacian and the fractional Laplacian. We also address some perspectives and open questions. Title: Variational Eigenvalues: Comparison between local and nonlocal operator Speaker: Sabri Bahrouni(UTM)

08/10/2020  ABSTRACT In this talk we shall consider a quasilinear elliptic problem involving the nonlocal pLaplacian operator. The main feature here is to exhibit a positive solution using the wellknown Nehari method, see [1]. At the end, we shall comment how these nonlocal elliptic problems have gained strength attention in the last few years, see also [2, 3]. Here also present some connections with the associated fibering maps, see for instance [4]. References [1] Lou, Q. Luo, H. Multiplicity and concentration of positive solutions for fractional p−Laplacian problem involving concaveconvex nonlinearity, Nonlinear analysis: Real world applications, 387405, 2018. [2] E. Di Nezza, G. Palatucci, E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces, Bulletin des sciences mathmatiques, 521573, 2012. [3] V. Ambrosio, Multiple solutions for a fractional pLaplacian equation with signchanging potential, Eletronic journal of differential equations, 112, 2016. [4] E. D da Silva, M. L. M. Carvalho, C. Goulart, Critical quasilinear elliptic problems using concaveconvex nonlinearities, Annali di matematica pura ed applicata, 693726, 2018. Title: Positive solutions for a fractional pLaplacian problem involving concaveconvex nonlinearity Speaker: Jefferson Luis Arruda Oliveira (IME/UFG) 
15/10/2020 
ABSTRACT
Title: Asymptotically periodic fourthorder Schrodinger equations with critical and subcritical growth Speaker: Claudiney Goulart(UFJ)
