Existence and multiplicity results for resonant fractional boundary value problems

We study a Dirichlet-type boundary value problem for a pseudo-differential equation driven by the fractional Laplacian, with a non-linear reaction term which is resonant at infinity between two non-principal eigenvalues: for such equation we prove existence of a non-trivial solution. Under further assumptions on the behavior of the reaction at zero, we detect at least three non-trivial solutions (one positive, one negative, and one of undetermined sign). All results are based on the properties of weighted fractional eigenvalues, and on Morse theory

Constant sign and nodal solutions for nonhomogeneous Robin boundary value problems with asymmetric reactions

We study a nonlinear, nonhomogeneous elliptic equation with an asymmetric reaction term depending on a positive parameter, coupled with Robin boundary conditions. Under appropriate hypotheses on both the leading differential operator and the reaction, we prove that, if the parameter is small enough, the problem admits at least four nontrivial solutions: two of such solutions are positive, one is negative, and one is sign-changing. Our approach is variational, based on critical point theory, Morse theory, and truncation techniques.Comment: 22 page

Multiple solutions for the fractional p-Laplacian with jumping reactions

We study a nonlinear elliptic equation driven by the degenerate fractional p-Laplacian, with Dirichlet-type condition and a jumping reaction, i.e., (p − 1)-linear both at infinity and at zero but with different slopes crossing the principal eigenvalue. Under two different sets of hypotheses, entailing different types of asymmetry, we prove the existence of at least two nontrivial solutions. Our method is based on degree theory for monotone operators and nonlinear fractional spectral theory

The Álvaro Siza’s master plan, the architectural and structural projects for the reconstruction of Chiado, in Lisbon

On 1988 a frightful fire broke out in Chiado, destroying 18 buildings, of which most part only the facades remained. A reconstruction plan was committed to Álvaro Siza, who fulfilled the request to preserve the existing buildings. The bibliography is mainly devoted to historical events, and architectural design options. There are few publications on the constructive and structural interventions, the objective of this study, to allow a broader knowledge about the intervention at various levels and disciplines. This is of particular interest in the scope of the research project “Siza Atlas. Filling the gaps for World Heritage” which aims to contribute to the nomination of a group of Siza's works for the World Heritage List. The subject is analyzed trough complementary readings: research of bibliography, documentation from the archive and in situ observations. A comparative analysis of the interventions proves a common method of construction with reinforced concrete structure built in situ. The principal improvement of the plan concerned the public space, recreating paths between the blocks, connecting the lower and upper levels of Chiado.info:eu-repo/semantics/publishedVersio

Existence, nonexistence and multiplicity of positive solutions for parametric nonlinear elliptic equations

We consider a parametric nonlinear elliptic equation driven by the Dirichlet p-Laplacian. We study the existence, nonexistence and multiplicity of positive solutions as the parameter varies in the set of positive reals and the potential exhibits a p-superlinear growth, without satisfying the usual in such cases Ambrosetti–Rabinowitz condition. We prove a bifurcation-type result when the reaction has (p-1)-sublinear terms near zero (problem with concave and convex nonlinearities). We show that a similar bifurcation-type result is also true, if near zero the right hand side is (p-1)-linear

Five solutions for the fractional p -Laplacian with noncoercive energy

We deal with a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction which satisfies, among other hypotheses, a (p- 1) -linear growth at infinity with non-resonance above the first eigenvalue. The energy functional governing the problem is thus noncoercive. We focus on the behavior of the reaction near the origin, assuming that it has a (p- 1) -sublinear growth at zero, vanishes at three points, and satisfies a reverse Ambrosetti–Rabinowitz condition. Under such assumptions, by means of critical point theory and Morse theory, and using suitably truncated reactions, we show the existence of five nontrivial solutions: two positive, two negative, and one nodal

The signalling channel of Central Bank interventions:modelling the Yen/US dollar exchange rate

This paper presents a theoretical framework analysing the signalling channel of exchange rate interventions as an informational trigger. We develop an implicit target zone framework with learning in order to model the signalling channel. The theoretical premise of the model is that interventions convey signals that communicate information about the exchange rate objectives of the central bank. The model is used to analyse the impact of Japanese FX interventions during the period 1999--2011 on the yen/US dollar dynamics

H^s versus C^0-weighted minimizers

We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology.Comment: 15 page

Guida alla redazione degli atti amministrativi

La "Guida alla redazione degli atti amministrativi" intende fornire indicazioni per la redazione degli atti per tutti i funzionari della pubblica amministrazione. Si articola in tre parti: (a) la lingua degli atti, (b) la struttura del provvedimento amministrativo, (c) il rinvio ad altri atti. Ne è autore un gruppo di linguisti e giuristi facenti capo all'ITTIG-CNR (Istituto per le Tecniche e Tecnologie dell'Informazione Giuridica) e dell'Accademia della Crusca