Flaviano Battelli
“Strongly Exponentially Separated Linear Systems”
Abstract: We present a theory of exponential separation which applies to unbounded systems. It turns out that in order to have a reasonable theory it is necessary to add the assumption that the angle between the two separated subspaces is bounded below (this is the strong exponential separation). Finally we apply the result to the study of upper triangular systems and prove that if a bounded linear Hamiltonian system is exponentially separated into two subspaces of the same dimension, then it must have an exponential dichotomy.
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Irene Benedetti
“Metodo delle funzioni di Lyapunov per problemi differenziali”
Abstract: L’utilizzo delle funzioni di Lyapunov permette di studiare l’esistenza e la localizzazione di soluzioni per equazioni differenziali con condizioni al bordo anche non locali. L’uso di questo strumento, in connessione con la teoria del grado topologico, porta alla dimostrazione di risultati di esistenza con condizioni di crescita molto generali sul termine nonlineare dell’equazione. Tale metodo è utile anche nel caso in cui ci siano impulsi variabili nel tempo, cioè problemi differenziali in cui la soluzione non è più una funzione continua, ma può presentare dei salti. Inizialmente introdotto in spazi finito dimensionali per soluzioni classiche, il metodo delle funzioni di Lyapunov si può estendere al caso infinito dimensionale e alla ricerca di soluzioni mild. In questo seminario, dopo una breve descrizione del metodo, verranno illustrati problemi differenziali, sia nonlocali, sia soggetti ad impulsi, affrontati con questo procedimento.
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Stefano Biagi
“Some existence results for boundary value problems associated with singular equations”
Abstract
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Gabriele Bonanno
“Two positive solutions for nonlinear problems”
Abstract: A two non-zero critical points theorem for differentiable functionals depending on a parameter is presented. It is based on a local minimum theorem and the mountain pass theorem. Some applications to nonlinear differential problems and some notes on the best value of the parameter for which the problem admits non-trivial solutions are highlighted.
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Pasquale Candito
“Esistenza di due o tre soluzioni per problemi differenziali non lineari”
Abstract: Lo scopo di questa conferenza è quello di presentare alcuni risultati di esistenza di almeno due o tre soluzioni per problemi nonlineari.
Il metodo variazionale utilizzato si basa su una combinazione di un teorema di minimo locale con il teorema del passo montano di Ambrosetti-Rabinowitz.
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Antonia Chinnì
“Existence of one non-zero solution for a two point boundary value problem involving a fourth-order equation”
Abstract
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Filomena Cianciaruso
“Semilinear Elliptic Systems with Dependence on the Gradient”
Abstract: In this talk, I present existence results of positive radial solutions for semilinear elliptic systems with Dirichlet or Robin boundary conditions on an annulus. The results are obtained by means of an approach based on fixed point index theory and invariance properties of a suitable cone, in which Harnack-type inequalities are used.
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Chiara Corsato
“Solvability of a MEMS model driven by capillarity and pressure effects”
Abstract
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Giuseppina D’Aguì
“Positive solutions to discrete two point nonlinear boundary value problems”
Abstract: In this talk, some results on the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p-Laplacian operator are presented. In particular, the existence of at least two solutions is obtained by requiring the p-superlinearity at infinity and the p-sublinearity at zero on the primitive of the nonlinear term. Our main tool is a two critical point theorem, obtained by an appropriate combination of the powerful classical Ambrosetti-Rabinowitz theorem with a recent non-zero local minimum theorem.
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Francesca Dalbono
“Multiplicity of ground states for the scalar curvature equation”
Abstract
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Beatrice Di Bella
“Variational approach to some boundary value problems with impulsive effects”
Abstract: In this talk we present some results concerning the existence of multiple solutions for a nonlinear boundary value problem subject to perturbations of impulsive terms.
Our method uses a local minimum theorem and a two non-zero critical points for differentiable functionals, introduced in [1].
Under suitable assumptions on the potential of the nonlinearity, the existence of one or two solutions is established.
[1] Bonanno G. and D’Aguì G., “Two non-zero solutions for elliptic Dirichlet problems”, Z. Anal. Anwend. 35 (2016), no. 4, 449-464.
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Alessandro Fonda
“An infinite-dimensional version of the Poincaré-Birkhoff theorem”
Abstract: We propose a version of the Poincaré-Birkhoff theorem for infinite-dimensional Hamiltonian systems. The twist condition, adapted to a Hilbert cube, is spread on a sequence of approximating finite-dimensional systems. By a limit procedure, the existence of at least one periodic solution is obtained.
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Oltiana Gjata
“Complicated dynamics in a model of charged particles”
Abstract: We present some recent results on chaotic dynamics of charged particles inside a toroidal confinement, such as the tokamak, in presence of plasma. In our model, after suitable changes of variables and assuming a small perturbation of the magnetic field, we can define suitably chosen rectangular regions which are linked together in a suitable manner. The existence of chaos (in the sense of semiconjugation to a full shift on a set of symbols), is proved by applying the theory of Linked Twist Maps and the stretching along the paths technique.
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Roberto Livrea
“Periodic, Dirichlet or homoclinic type solutions for second order boundary value problems”
Abstract: The talk is focused on an overview of some existence and multiplicity results for two different types of second order, one dimensional, differential problems. In particular, some theorems dealing with some classes of second order, periodic, Hamiltonian systems will be shown. Moreover, a nonlinear singular equation with not variational structure will be presented, emphasizing the existence of either Dirichlet type solutions or homoclinic positive solutions.
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Luisa Malaguti
“Viscous profiles in models of collective movements with negative diffusivities”
Abstract: The talk deals with an advection-diffusion equation whose diffusivity can be negative. Such equations arise in particular in the modeling of vehicular traffic flows or crowds dynamics, where a negative diffusivity simulates aggregation phenomena. We focus on traveling-wave solutions that connect two states whose diffusivity has different signs; under some geometric conditions we prove the existence, uniqueness (in a suitable class of solutions avoiding plateaus) and sharpness of the corresponding profiles. Such results are then extended to the case of end states where the diffusivity is positive but it becomes negative in some interval between them. Also the limit behaviour of these traveling-wave solutions when the diffusivity goes to zero, i.e. the vanishing-viscosity limit, is considered. At last, we discuss some examples of diffusivities that change sign and show that our conditions are satisfied for most of them in correspondence of real data. This discussion mainly comes from: A. Corli – L. Malaguti “Viscous profiles in models of collective movements with negative diffusivities”, submitted.
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Salvatore Marano
“L.s.c. differential inclusions with p-Laplacian”
Abstract: the existence of solutions to lower semi-continuous closed-valued differential inclusions with p-Laplacian is investigated under various growth conditions. Proofs exploit the Bressan-Colombo-Fryszkowski continuous selection theorem and fixed point arguments. Some consequences are then pointed out.
Sunra Mosconi
“Parabolic equations with slow diffusion”
Abstract: A parabolic equation has the slow diffusion property if compactly supported initial data propagate along the flow at finite speed. This can be caused either by absorption effects in the medium or by some degeneracy in the intrinsic diffusivity properties of the latter.
We will overview some known results of both types and focus on new ones involving parabolic problems where slow diffusion is caused by a heavy anisotropy in the material.
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Luigi Muglia
“An existence result for a new class of impulsive functional differential equations with delay”
Abstract: The literature regarding impulsive differential equations is wide and rich; this is due to the intrinsic difficulties and the variety of the problems, and also to the impressive amount of applications in different branches of Science. Indeed, impulsive differential equations naturally arise from several frameworks like pulse vaccination strategy or processes of fed-batch fermentation. We will prove the existence of bounded solutions of a new class of retarded functional differential equations with non-instantaneous impulses and delay on an unbounded domain. An application example is also included.
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Pierpaolo Omari
“Global components of positive bounded variation solutions of a one-dimensional indefinite quasilinear Neumann problem”
Abstract
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Maria Patrizia Pera
“Molteplicità di oscillazioni forzate per equazioni differenziali del second’ordine con ritardo”
In questa presentazione verranno illustrati alcuni risultati di molteplicità di soluzioni periodiche per equazioni del second’ordine con ritardo finito o di tipo funzionale. Essi sono stati ottenuti recentemente in collaborazione con A. Calamai e M. Spadini.
L’approccio considerato è di tipo topologico (si fa uso principalmente della nozione di grado di un campo vettoriale tangente) ed è basato su alcune proprietà di continuazione globale dell’insieme delle soluzioni.
Come esempi, verranno interpretati i risultati nel caso di un’equazione scalare e in quello del pendolo sferico (moto di un punto materiale vincolato su una sfera).
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Marco Sabatini
“Measure-preserving symmetries and reversibilities of ordinary differential systems”
Abstract: We prove that measure-preserving symmetries of an n-dimensional differential system preserve its divergence and the divergence derivatives along the solutions. Also, we prove that measure-preserving reversibilities preserve odd-order divergence derivatives along the solutions, and that even-order derivatives are multiplied by −1. We apply such results to find all the area-preserving symmetries and reversibilities of planar Lotka-Volterra and Liénard systems.
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Angela Sciammetta
“Nonlinear boundary value problems with variable exponent”
Abstract: In this talk, a class of nonlinear differential boundary value problems with variable exponent is presented. The existence of at least one nonzero solution is established, without assuming on the nonlinear term any condition either at zero or at infinity. The approach is developed within the framework of the Orlicz-Sobolev spaces with variable exponent and it is based on a local minimum theorem for differentiable functions.
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Andrea Sfecci
“Risultati di esistenza di soluzioni in problemi prossimi alla risonanza”
Abstract: Saranno presentati diversi risultati di esistenza per problemi ai limiti di equazioni differenziali ordinarie in cui la nonlinearità è asintoticamente risonante. Saranno mostrate situazioni in cui si verifica la cosiddetta doppia risonanza. I risultati di esistenza si possono ottenere mediante l’introduzione di condizioni tipo Landesman-Lazer. Sarà presentata una carrellata su alcuni recenti risultati che coinvolgono questo tipo di approccio.
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Elisa Sovrano
“About indefinite Neumann problems with oscillating nonlinear potentials: multiplicity of positive solutions”
Abstract
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Elisabetta Tornatore
“Existence results for Sturm-Liouville equations with mixed boundary conditions”
Abstract
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Fabio Zanolin
“Multiple periodic solutions for one-sided sublinear systems: A
refinement of the Poincaré-Birkhoff approach”
Abstract: We prove the existence of multiple periodic solutions (harmonics
and subharmonics) for a class of planar Hamiltonian systems which
include the case of the second order scalar ODE
x” + a(t)g(x) =0
with g satisfying a one-side condition of sublinear type. We
consider the classical approach based on the Poincaré-Birkhoff
fixed point theorem as well as some refinements on the side of the
theory of bend-twist maps. The case of complex dynamics is
investigated, too.
This is a joint work with Tobia Dondè (University of Udine).
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