arXiv subjects

G. Siciliano

Publications and source records attributed to G. Siciliano.

4 recordsLinked to original sources

arXiv2021

Hartree-Fock type systems: existence of ground states and asymptotic behavior

In this paper we consider an Hartree-Fock type system made by two Schrödinger equations in presence of a Coulomb interacting term and a cooperative pure power and subcritical nonlinearity, driven by a suitable parameter $β\geq 0$. We show the existence of semitrivial and vectorial ground states solutions depending on the parameters involved. The asymptotic behavior with respect to the parameter $β$ of these solutions is also studied.

math.AP↗

arXiv2016

Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain

We prove existence of multiple positive solutions for a {\sl fractional scalar field equation} in a bounded domain, whenever $p$ tends to the critical Sobolev exponent. By means of the "photography method", we prove that the topology of the domain furnishes a lower bound on the number of positive solutions.

math.AP↗

arXiv2015

Multiplicity results for the fractional laplacian in expanded domains

In this paper we establish the multiplicity of nontrivial weak solutions for the problem $(-Δ)^α u +u= h(u)$ in $Ω_λ$,\ $u=0$ on $\partialΩ_λ$, where $Ω_λ=λΩ$, $Ω$ is a smooth and bounded domain in $\mathbb{R}^N, N>2α$, $λ$ is a positive parameter, $α\in (0,1)$, $(-Δ)^α$ is the fractional Laplacian and the nonlinear term $h(u)$ has a subcritical growth. We use minimax methods, the Ljusternick-Schnirelmann and Morse theories to get multiplicity result depending on the topology of $Ω$.

math.AP↗

arXiv2008

Magneto-static vortices in two dimensional Abelian gauge theories

We study the existence of vortices of the Klein-Gordon-Maxwell equations in the two dimensional case. In particular we find sufficient conditions for the existence of vortices in the magneto-static case, i.e when the electric potential $ϕ=0$. This result, due to the lack of suitable embedding theorems for the vector potential $\A$ is achieved with the help of a penalization method.

math.AP↗