Benedetta Pellacci
YOU?
Author Swipe
View article: Asymptotic location and shape of the optimal favorable region in a Neumann spectral problem
Asymptotic location and shape of the optimal favorable region in a Neumann spectral problem Open
We complete the study concerning the minimization of the positive principal eigenvalue associated with a weighted Neumann problem settled in a bounded regular domain $Ω\subset \mathbb{R}^{N}$, $N\ge2$, for the weight varying in a suitable …
View article: Partially concentrating standing waves for weakly coupled Schrödinger systems
Partially concentrating standing waves for weakly coupled Schrödinger systems Open
We study the existence of standing waves for the following weakly coupled system of two Schrödinger equations "Equation missing"where $$V_1$$ and $$V_2$$ are radial potentials bounded from below. We address the case "Equation missi…
View article: An upper bound for the least energy of a sign-changing solution to a zero mass problem
An upper bound for the least energy of a sign-changing solution to a zero mass problem Open
We give an upper bound for the least possible energy of a sign-changing solution to the nonlinear scalar field equation − Δ u = f ( u ) , u ∈ D 1,2 ( R N ) , $-{\Delta}u=f\left(u\right), u\in {D}^{1,2}\left({\mathrm{R}}^{N}\righ…
View article: Partially concentrating standing waves for weakly coupled Schrödinger systems
Partially concentrating standing waves for weakly coupled Schrödinger systems Open
We study the existence of standing waves for the following weakly coupled system of two Schrödinger equations in $\mathbb{R}^N$, $N=2,3$, \[ \begin{cases} i \hslash \partial_{t}ψ_{1}=-\frac{\hslash^2}{2m_{1}}Δψ_{1}+ {V_1}(x)ψ_{1}-μ_{1}|ψ_{…
View article: Singular Analysis of the Optimizers of the Principal Eigenvalue in Indefinite Weighted Neumann Problems
Singular Analysis of the Optimizers of the Principal Eigenvalue in Indefinite Weighted Neumann Problems Open
We study the minimization of the positive principal eigenvalue associated to aweighted Neumann problem settled in a bounded smooth domain \Omega \subset \BbbR N,N\geq 2, within a suitableclass of sign-changing weights. This problem arises …
View article: Spectral optimization for weighted anisotropic problems with Robin conditions
Spectral optimization for weighted anisotropic problems with Robin conditions Open
We study a weighted eigenvalue problem with anisotropic diffusion in bounded Lipschitz domains $Ω\subset \mathbb{R}^{N} $, $N\ge1$, under Robin boundary conditions, proving the existence of two positive eigenvalues $λ^{\pm}$ respectively a…
View article: An upper bound for the least energy of a sign-changing solution to a zero mass problem
An upper bound for the least energy of a sign-changing solution to a zero mass problem Open
We give an upper bound for the least energy of a sign-changing solution to the the nonlinear scalar field equation $$-Δu = f(u), \qquad u\in D^{1,2}(\mathbb{R}^{N}),$$ where $N\geq5$ and the nonlinearity $f$ is subcritical at infinity and …
View article: Singular analysis of the optimizers of the principal eigenvalue in indefinite weighted Neumann problems
Singular analysis of the optimizers of the principal eigenvalue in indefinite weighted Neumann problems Open
We study the minimization of the positive principal eigenvalue associated to a weighted Neumann problem settled in a bounded smooth domain $Ω\subset \mathbb{R}^{N}$, within a suitable class of sign-changing weights. Denoting with $u$ the o…
View article: Symmetric positive solutions to nonlinear Choquard equations with potentials
Symmetric positive solutions to nonlinear Choquard equations with potentials Open
Existence results for a class of Choquard equations with potentials are established. The potential has a limit at infinity and it is taken invariant under the action of a closed subgroup of linear isometries of $\mathbb{R}^N$. As a consequ…
View article: Positive bound states to nonlinear Choquard equations in the presence of nonsymmetric potentials
Positive bound states to nonlinear Choquard equations in the presence of nonsymmetric potentials Open
The existence of a positive solution to a class of Choquard equations with potential going at a positive limit at infinity possibly from above or oscillating is proved. Our results include the physical case and do not require any symmetry …
View article: Asymptotic behavior of positive solutions of semilinear elliptic problems with increasing powers
Asymptotic behavior of positive solutions of semilinear elliptic problems with increasing powers Open
We prove existence results of two solutions of the problem \[ \begin{cases} L(u)+u^{m-1}=λu^{p-1} & \text{ in $Ω$}, \\ \quad u>0 &\text{ in $Ω$}, \\ \quad u=0 & \text{ on $\partial Ω$}, \end{cases} \] where $L(v)=-{\rm div}(M(x)\nabla v)$ …
View article: Normalized concentrating solutions to nonlinear elliptic problems
Normalized concentrating solutions to nonlinear elliptic problems Open
We prove the existence of solutions (λ,v)∈R×H1(Ω) of the elliptic problem {−Δv+(V(x)+λ)v=vp in Ω,v>0,∫Ωv2dx=ρ. Any v solving such problem (for some λ) is called a normalized solution, where the normalization is settled in L2(Ω). Here Ω …
View article: Time-fractional equations with reaction terms: Fundamental solutions and asymptotics
Time-fractional equations with reaction terms: Fundamental solutions and asymptotics Open
We analyze the fundamental solution of a time-fractional problem, establishing existence and uniqueness in an appropriate functional space. We also focus on the one-dimensional spatial setting in the case in which the time-fractional expon…
View article: Asymptotic spherical shapes in some spectral optimization problems
Asymptotic spherical shapes in some spectral optimization problems Open
We study the optimization of the positive principal eigenvalue of an indefinite weighted problem, associated with the Neumann Laplacian in a box Ω⊂RN, which arises in the investigation of the survival threshold in population dynamics. When…
View article: Quantitative analysis of a singularly perturbed shape optimization\n problem in a polygon
Quantitative analysis of a singularly perturbed shape optimization\n problem in a polygon Open
We carry on our study of the connection between two shape optimization\nproblems with spectral cost. On the one hand, we consider the optimal design\nproblem for the survival threshold of a population living in a heterogenous\nhabitat $\\O…
View article: Oscillating solutions for nonlinear nonlinear Helmholtz equations
Oscillating solutions for nonlinear nonlinear Helmholtz equations Open
Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behavior at infinity is established. Some generalizations to nonautonomous radial e…
View article: Best dispersal strategies in spatially heterogeneous environments: optimization of the principal eigenvalue for indefinite fractional Neumann problems
Best dispersal strategies in spatially heterogeneous environments: optimization of the principal eigenvalue for indefinite fractional Neumann problems Open
We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian. This analysis is related to the investigation of the survival threshold in population dynamics. Our main result con…
View article: Optimization of the positive principal eigenvalue for indefinite fractional Neumann problems
Optimization of the positive principal eigenvalue for indefinite fractional Neumann problems Open
We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian. This analysis is related to the investigation of the survival threshold in population dynamic. Our main result conc…
View article: Best dispersal strategies in spatially heterogeneous environments:\n optimization of the principal eigenvalue for indefinite fractional Neumann\n problems
Best dispersal strategies in spatially heterogeneous environments:\n optimization of the principal eigenvalue for indefinite fractional Neumann\n problems Open
We study the positive principal eigenvalue of a weighted problem associated\nwith the Neumann spectral fractional Laplacian. This analysis is related to the\ninvestigation of the survival threshold in population dynamics. Our main result\n…