80 citations · 243 across the 22 of their papers we have counts for
14 papers · 1 filter
Action versus energy ground states in nonlinear Schrödinger equations
Simone Dovetta, Enrico Serra, Paolo Tilli
We investigate the relations between normalized critical points of the nonlinear Schrödinger energy functional and critical points of the corresponding action functional on the ass…
A minimization procedure to the existence of segregated solutions to parabolic reaction-diffusion systems
Alessandro Audrito, Enrico Serra, Paolo Tilli
We study the existence of segregated solutions to a class of reaction-diffusion systems with strong interactions, arising in many physical applications. These special solutions are…
Uniqueness and non-uniqueness of prescribed mass NLS ground states on metric graphs
Simone Dovetta, Enrico Serra, Paolo Tilli
We consider the problem of uniqueness of ground states of prescribed mass for the Nonlinear Schrödinger Energy with power nonlinearity on noncompact metric graphs. We first establi…
NLS ground states on metric trees: existence results and open questions
Simone Dovetta, Enrico Serra, Paolo Tilli
We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric…
Dimensional crossover with a continuum of critical exponents for NLS on doubly periodic metric graphs
Riccardo Adami, Simone Dovetta, Enrico Serra +1
We investigate the existence of ground states for the focusing nonlinear Schroedinger equation on a prototypical doubly periodic metric graph. When the nonlinearity power is below…
An existence result for dissipative nonhomogeneous hyperbolic equations via a minimization approach
Lorenzo Tentarelli, Paolo Tilli
We discuss a purely variational approach to the study of a wide class of second order nonhomogeneous dissipative hyperbolic PDEs. Precisely, we focus on the wave-like equations tha…
Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length
Paolo Tilli, Davide Zucco
We consider the problem of maximizing the first eigenvalue of the -laplacian (possibly with non-constant coefficients) over a fixed domain , with Dirichlet conditions along $…
De Giorgi's approach to hyperbolic Cauchy problems: the case of nonhomogeneous equations
Lorenzo Tentarelli, Paolo Tilli
In this paper we discuss an extension of some results obtained by E. Serra and P. Tilli, in [Serra&Tilli '12, Serra&Tilli '16], concerning an original conjecture by E. De Giorgi ([…
Multiple positive bound states for the subcritical NLS equation on metric graphs
Riccardo Adami, Enrico Serra, Paolo Tilli
We consider the Schroedinger equation with a subcritical focusing power nonlinearity on a noncompact metric graph, and prove that for every finite edge there exists a threshold val…
Nonlinear dynamics on branched structures and networks
Riccardo Adami, Enrico Serra, Paolo Tilli
Nonlinear dynamics on graphs has rapidly become a topical issue with many physical applications, ranging from nonlinear optics to Bose-Einstein condensation. Whenever in a physical…
Threshold phenomena and existence results for NLS ground states on graphs
Riccardo Adami, Enrico Serra, Paolo Tilli
We investigate the existence of ground states of prescribed mass, for the nonlinear Schroedinger energy on a noncompact metric graph G. While in some cases the topology of G may ru…
NLS ground states on graphs
Riccardo Adami, Enrico Serra, Paolo Tilli
We investigate the existence of ground states for the subcritical NLS energy on metric graphs. In particular, we find out a topological assumption that guarantees the nonexistence…
Lack of ground state for NLS on bridge-type graphs
Riccardo Adami, Enrico Serra, Paolo Tilli
We prove the nonexistence of ground states for NLS on bridge-like graphs, i.e. graphs with two halflines and four vertices, of which two at infinity, with Kirchhoff matching condit…
A minimization approach to hyperbolic Cauchy problems
Enrico Serra, Paolo Tilli
Developing an original idea of De Giorgi, we introduce a new and purely variational approach to the Cauchy Problem for a wide class of defocusing hyperbolic equations. The main nov…