Search results for "Analisi Matematica"
showing 10 items of 811 documents
Nonlinear multivalued Duffing systems
2018
We consider a multivalued nonlinear Duffing system driven by a nonlinear nonhomogeneous differential operator. We prove existence theorems for both the convex and nonconvex problems (according to whether the multivalued perturbation is convex valued or not). Also, we show that the solutions of the nonconvex problem are dense in those of the convex (relaxation theorem). Our work extends the recent one by Kalita-Kowalski (JMAA, https://doi.org/10.1016/j.jmaa. 2018.01.067).
Existence and Relaxation Results for Second Order Multivalued Systems
2021
AbstractWe consider nonlinear systems driven by a general nonhomogeneous differential operator with various types of boundary conditions and with a reaction in which we have the combined effects of a maximal monotone term $A(x)$ A ( x ) and of a multivalued perturbation $F(t,x,y)$ F ( t , x , y ) which can be convex or nonconvex valued. We consider the cases where $D(A)\neq \mathbb{R}^{N}$ D ( A ) ≠ R N and $D(A)= \mathbb{R}^{N}$ D ( A ) = R N and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.
Remarks on Infinite-Dimensional Representations of the Heisenberg Algebra
2017
Infinite-dimensional representations of Lie algebras necessarily invoke the theory of unbounded operator algebras. Starting with the familiar example of the Heisenberg Lie algebra, we sketch the essential features of this interaction, distinguishing in particular the cases of integrable and nonintegrable representations. While integrable representations are well understood, nonintegrable representations are quite mysterious objects. We present here a short and didactical-minded overview of the subject.
On the stability of the localized single-valued extension property under commuting perturbations
2013
This article concerns the permanence of the single-valued extension property at a point under suitable perturbations. While this property is, in general, not preserved under sums and products of commuting operators, we obtain positive results in the case of commuting perturbations that are quasi-nilpotent, algebraic, or Riesz operators.
Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem
2011
Abstract We determine the shape which minimizes, among domains with given measure, the first eigenvalue of a nonlocal operator consisting of a perturbation of the standard Dirichlet Laplacian by an integral of the unknown function. We show that this problem displays a saturation behaviour in that the corresponding value of the minimal eigenvalue increases with the weight affecting the average up to a (finite) critical value of this weight, and then remains constant. This critical point corresponds to a transition between optimal shapes, from one ball as in the Faber–Krahn inequality to two equal balls.
Sesquilinear forms associated to sequences on Hilbert spaces
2019
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation theorems of sesquilinear forms, such as Kato's theorems. The associated operators correspond to classical frame operators or weakly-defined multipliers in the bounded context. In general some properties of them, such as the invertibility and the resolvent set, are related to properties of the sesquilinear forms. As an upshot of this approach new features of sequences (or pairs of sequences) which are semi-frames (or reproducing pairs) are obtained.
A sequence of positive solutions for sixth-order ordinary nonlinear differential problems
2021
Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.
Set valued integrability in non separable Fréchet spaces and applications
2016
AbstractWe focus on measurability and integrability for set valued functions in non-necessarily separable Fréchet spaces. We prove some properties concerning the equivalence between different classes of measurable multifunctions. We also provide useful characterizations of Pettis set-valued integrability in the announced framework. Finally, we indicate applications to Volterra integral inclusions.
Non-Hermitian Hamiltonians in Quantum Physics
2016
This volume collects the selected contributions presented at or inspired by the15th International Workshop on Pseuso-Hermitian Hamiltonians in QuantumPhysics(PHHQP15), held in Palermo, Italy, from May 18 to 23, 2015. Thisworkshop was the 15th in the series of international meetings that was started in2003. These meetings were mainly attended by mathematicians and physicistsinterested in the study of non-Hermitian operators and Hamiltonians, and in theirphysical applications. About 80 mathematicians and physicists attended the 2015Workshop in Palermo.
Probability of mutually commuting n-tuples in some classes of compact groups
2008
In finite groups the probability that two randomly chosen elements commute or randomly ordered n−tuples of elements mutually commute have recently attracted interest by many authors. There are some classical results estimating the bounds for this kind of probability so that the knowledge of the whole structure of the group can be more accurate. The same problematic has been recently extended to certain classes of infinite compact groups in [2], obtaining restrictions on the group of the inner automorphisms. Here such restrictions are improved for a wider class of infinite compact groups.