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International Workshop on

Topological and Variational Methods for ODEs

Dedicated to Massimo Furi Professor Emeritus at the University of Florence

Firenze, Dipartimento di Matematica e Informatica "U. Dini", June 3 - 4, 2014


Opening: June 3rd, 2:30 pm --- Closing: June 4th, 1:00 pm



Schedule

Tuesday, June 3
14:00 - 14:30Registration
14:30 - 14:45Welcome ceremony: Greetings by the rector Alberto Tesi and by DIMAI's director Giuseppe Anichini
14:45 - 15:15Fabio Zanolin, Università di Udine, Multiple positive solutions for superlinear equations with a sign-indefinite weight
15:20 - 15:50 Pierluigi Benevieri, Universidade de São Paulo, On the oriented degree for multivalued compact perturbations of Fredholm maps in Banach spaces
15:55 - 16:25 Zuzana Došlá, Masaryk University - Brno, On the generalized Emden-Fowler differential equation
16:30 - 17:00Coffee break
17:00 - 17:30 Jacobo Pejsachowicz, Politecnico di Torino, Bifurcation of critical points for continuous families of C2 functionals of Fredholm type
17:35 - 18:05 Alessandro Calamai, Università Politecnica delle Marche, Global continuation of periodic solutions for retarded functional differential equations on manifolds
20:20Social dinner
Wednesday, June 4
9:15 - 9:45Alessandro Fonda, Università di Trieste, The Poincaré - Birkhoff theorem in the framework of Hamiltonian systems
9:50 - 10:20Anna Capietto, Università di Torino, A global bifurcation result for a second order singular equation
10:25 - 10:55Gennaro Infante, Università della Calabria, Nontrivial solutions of local and nonlocal Neumann boundary value problems
11:00 - 11:30Coffee break
11:30 - 12:00Gabriele Bonanno, Università di Messina, A local minimum theorem and nonlinear differential problems
12:05 - 12:35Pierpaolo Omari, Università di Trieste, An asymmetric Poincaré inequality and applications
12:35 - 12:40Closing




Titles and abstracts

Scheduled talks:
Pierluigi Benevieri Title: On the oriented degree for multivalued compact perturbations of Fredholm maps in Banach spaces
Abstract: We discuss a concept of oriented topological degree for locally compact multivalued perturbations of Fredholm maps in Banach spaces. The construction is based on a notion of orientation for nonlinear Fredholm maps and on a finite dimensional reduction approach. We see an application to an existence problem for nonlinear differential inclusions.
SLIDES
Gabriele Bonanno Title: A local minimum theorem and nonlinear differential problems
Abstract: A local minimum theorem for differentiable functionals is presented and a characterization of the mountain pass geometry is pointed out. As an application, existence and multiplicity results for nonlinear differential problems are obtained.
SLIDES
Alessandro Calamai Title: Global continuation of periodic solutions for retarded functional differential equations on manifolds
Abstract: In 1990, Furi and Pera proved the existence of forced oscillations for the spherical pendulum. For this purpose they studied a one-parameter constrained motion problem associated to a T-periodic parametrized force.
Here we will discuss the extension of the results of Furi and Pera to the case of retarded functional differential equations with infinite delay on differentiable manifolds, as well as applications to the retarded spherical pendulum.
SLIDES
Anna Capietto Title: A global bifurcation result for a second order singular equation
Abstract: We deal with a boundary value problem associated to a second order singular equation in the open interval (0,1]. We first study the eigenvalue problem in the linear case and discuss the nodal properties of the eigenfunctions. We then give a global bifurcation result for nonlinear problems.
SLIDES
Zuzana Došlá Title: On the generalized Emden-Fowler differential equation
Abstract: The problem of the oscillatory and asymptotic behavior of solutions for Emden-Fowler equations has a long history. It started almost 60 years ago when Atkinson published in Pacific J. Math. his famous paper "On second order non-linear oscillations". This history continued in 1959 by Moore & Nehari, in nineties of the last century by Kusano, Elbert et al. and recently, by Kamo & Usami, Naito and Cecchi-D-Marini.
In this talk, we completely resolve the problem on the coexistence of solutions with different growth at infinity. Moreover, in the super-linear case, necessary and sufficient conditions for the existence of the so-called slowly increasing solutions are given too. Observe that, until now, due the lack of sharp upper and lower bounds, their existence was an open problem.
This is a joint work with Mauro Marini, University of Florence.
SLIDES
Alessandro Fonda Title: The Poincaré - Birkhoff theorem in the framework of Hamiltonian systems
Abstract: The theorem, conjectured by Poincaré in 1912 and proved by Birkhoff some years later, was originally stated for a two-dimensional annulus. We propose some extensions to higher dimensions for Poincaré time-maps of Hamiltonian systems. Our results apply to pendulum-type systems and weakly-coupled superlinear systems.
SLIDES
Gennaro Infante Title: Nontrivial solutions of local and nonlocal Neumann boundary value problems
Abstract: We discuss new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed point index. Some of the criteria involve a comparison with the spectral radius of some related linear operators. We apply our results to some boundary value problems with local and nonlocal boundary conditions of Neumann type. We illustrate in some examples the methodologies used.
SLIDES
Pierpaolo Omari Title: An asymmetric Poincaré inequality and applications
Abstract: This talk is divided into two parts: first we prove an asymmetric version of the Poincaré inequality in the space of bounded variation functions; second, based on this result, we discuss the existence of bounded variation solutions of a class of capillarity problems with possibly asymmetric perturbations.
SLIDES
Jacobo Pejsachowicz Title: Bifurcation of critical points for continuous families of C2 functionals of Fredholm type
Abstract: I will review a joint paper with Nils Waterstraat which improves in many aspects an old result about the relation of the spectral flow with variational bifurcation and will discuss some of its applications in problems where strongly indefinite functionals arise.
SLIDES
Fabio Zanolin Title: Multiple positive solutions for superlinear equations with a sign-indefinite weight
Abstract: We study the existence and multiplicity of positive solutions for the Dirichlet boundary value problem associated to a class of second order nonlinear equations with a sign-indefinite weight, including the case u'' + a(x) g(u) = 0, with g(u) having superlinear growth at zero and at infinity and a(x) of nonconstant sign. We present some classical result, different approaches to the problem, as well as recent developments obtained with G. Feltrin from SISSA, Trieste.
SLIDES
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