Search results for "online"
showing 10 items of 4526 documents
La responsabilità dei prestatori di servizi di condivisione di contenuti online.
2023
Il saggio analizza il recepimento della dir. 2019/790/UE, sul diritto d'autore e i diritti connessi nel mercato unico digitale. Lo studio si concentra sulle norme relative alla responsabilità dei prestatori di servizi di condivisione di contenuti on-line e le confronta con le disposizioni generali contenute nel Digital Services Act. The essay analyzes the transposition of dir. 2019/790/EU, on copyright and related rights in the digital single market. The study focuses on the liability rules of online content sharing service providers and compares them with the general provisions contained in the Digital Services Act.
(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms
2018
We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian ($$p>2$$) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric $$(p-1)$$-linear term which is resonant as $$x \rightarrow - \infty $$, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.
Triple solutions for nonlinear elliptic problems driven by a non-homogeneous operator
2020
Abstract Some multiplicity results for a parametric nonlinear Dirichlet problem involving a nonhomogeneous differential operator of p -Laplacian type are given. Via variational methods, the article furnishes new contributions and completes some previous results obtained for problems considering other types of differential operators and/or nonlinear terms satisfying different asymptotic conditions.
Positive solutions for singular (p, 2)-equations
2019
We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a $$(p-1)$$ -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.
Some qualitative properties for the total variation flow
2002
We prove the existence of a finite extinction time for the solutions of the Dirichlet problem for the total variation flow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in finite time. The asymptotic profile of the solutions of the Dirichlet problem is also studied. It is shown that the profiles are nonzero solutions of an eigenvalue-type problem that seems to be unexplored in the previous literature. The propagation of the support is analyzed in the radial case showing a behaviour entirely different to the case of the problem associated with the p-Laplacian operator. Finally, the study of the radially symmetric case allows us to point out othe…
An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities
2005
AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.
Multiple solutions for a Dirichlet problem with p-Laplacian and set-valued nonlinearity
2008
AbstractThe existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via sub- and supersolution methods as well as variational techniques for nonsmooth functions.
Elliptic problems with convection terms in Orlicz spaces
2021
Abstract The existence of a solution to a Dirichlet problem, for a class of nonlinear elliptic equations, with a convection term, is established. The main novelties of the paper stand on general growth conditions on the gradient variable, and on minimal assumptions on Ω. The approach is based on the method of sub and supersolutions. The solution is a zero of an auxiliary pseudomonotone operator build via truncation techniques. We present also some examples in which we highlight the generality of our growth conditions.
Nonlinear elliptic equations having a gradient term with natural growth
2006
Abstract In this paper, we study a class of nonlinear elliptic Dirichlet problems whose simplest model example is: (1) { − Δ p u = g ( u ) | ∇ u | p + f , in Ω , u = 0 , on ∂ Ω . Here Ω is a bounded open set in R N ( N ⩾ 2 ), Δ p denotes the so-called p-Laplace operator ( p > 1 ) and g is a continuous real function. Given f ∈ L m ( Ω ) ( m > 1 ), we study under which growth conditions on g problem (1) admits a solution. If m ⩾ N / p , we prove that there exists a solution under assumption (3) (see below), and that it is bounded when m > N p ; while if 1 m N / p and g satisfies the condition (4) below, we prove the existence of an unbounded generalized solution. Note that no smallness condit…
Radial solutions of Dirichlet problems with concave-convex nonlinearities
2011
Abstract We prove the existence of a double infinite sequence of radial solutions for a Dirichlet concave–convex problem associated with an elliptic equation in a ball of R n . We are interested in relaxing the classical positivity condition on the weights, by allowing the weights to vanish. The idea is to develop a topological method and to use the concept of rotation number. The solutions are characterized by their nodal properties.