18 citations · 107 across the 28 of their papers we have counts for
36 papers
New sign-changing solutions to the Hénon problem in dimension
Francesca Gladiali, Pingping Yang
In this paper, we construct new sign-changing solutions for the Hénon problem \begin{equation*} \begin{cases} -Δu= |x|^α |u|^{p-1}u,\,\,\,\text{in}\,\,\, Ω, \\[1mm] u=0,\,\,\,\,\,\…
Optimization of the total tumor population under Gompertz growth
Iulia Martina Bulai, Francesca Gladiali, Benedetta Pellacci
We study optimal control problems for a stationary reaction--diffusion model describing the spatial distribution of a tumor cell population with Gompertz growth. The control …
Qualitative analysis on the critical points of the Kirchhoff-Routh function
Francesca Gladiali, Massimo Grossi, Peng Luo +1
In this paper, we study the number of critical points of the Kirchhoff-Routh function \begin{equation*} \mathcal{KR}_D(x,y)=Λ_1^2\mathcal{R}_D(x)+Λ_2^2\mathcal{R}_D(y)-2Λ_1Λ_2G_D(x…
The role of the curvature of a surface in the shape of the solutions to elliptic equations
Francesca Gladiali, Massimo Grossi, Luigi Provenzano
We prove uniqueness and non-degeneracy of the critical point of positive, semi-stable solutions of with Dirichlet boundary conditions for a class of star-shaped domains…
Solutions to general elliptic equations on nearly geodesically convex domains with many critical points
Alberto Enciso, Francesca Gladiali, Massimo Grossi
Consider a complete -dimensional Riemannian manifold , a point and a nonlinearity with . We prove that for any odd integer $N…
On the critical points of solutions of PDE in a non-convex settings: the case of concentrating solutions
Francesca Gladiali, Massimo Grossi
In this paper we are concerned with the number of critical points of solutions of nonlinear elliptic equations. We will deal with the case of non-convex, contractile and non-contra…
Qualitative analysis on the critical points of the Robin function
Francesca Gladiali, Massimo Grossi, Peng Luo +1
Let be a smooth bounded domain with and where is the ball centered at and radius . In this paper, we est…
Symmetry and monotonicity results for solutions of semilinear PDEs in sector-like domains
Antonio Greco, Francesca Gladiali
In this manuscript we consider semilinear PDEs, with a convex nonlinearity, in a sector-like domain. Using cylindrical coordinates , we investigate the shape of solution…
A complete scenario on nodal radial solutions to the Brezis Nirenberg problem in low dimensions
Annalisa Amadori, Francesca Gladiali, Massimo Grossi +2
In this paper we consider nodal radial solutions of the problem where $2^*=\frac{2N}{N…
Bifurcation analysis of the Hardy-Sobolev equation
Denis Bonheure, Jean-Baptiste Casteras, Francesca Gladiali
In this paper, we prove existence of multiple non-radial solutions to the Hardy-Sobolev equation $$\begin{cases} -Δu-\displaystyle\frac γ{|x|^2}u=\displaystyle\frac{1}{|x|^s}|u|^{p…
A note on nonradial nodal solutions to the Hénon problem in the disc
Francesca Gladiali, Giovanni Stegel
In this paper we consider some nodal solutions of the Hénon problem in the unit disc with Dirichlet boundary conditions and we show that they are quasiradial, that is to say they a…
Asymptotic behavior of minimal solutions of as
Luca Battaglia, Francesca Gladiali, Massimo Grossi
We consider the Dirichlet problem with and non-negative and non-decreasing. We show existence and uniqueness of solutions for any and discuss their…
On the number of critical points of solutions of semilinear equations in
Francesca Gladiali, Massimo Grossi
In this paper we construct families of bounded domains and solutions of \[\begin{cases} -Δu_\varepsilon=1&\text{ in }\ Ω_\varepsilon\\ u_\varepsilon…
On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE's, Part II
Anna Lisa Amadori, Francesca Gladiali
By using a characterization of the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem given in a previous paper, we give a lower bound for the…
The Hénon problem with large exponent in the disc
Anna Lisa Amadori, Francesca Gladiali
In this paper we consider the Hénon problem in the unit disc with Dirichlet boundary conditions. We study the asymptotic profile of least energy and nodal least energy radial solut…
A monotonicity result under symmetry and Morse index constraints in the plane
Francesca Gladiali
This paper deals with solutions of semilinear elliptic equations of the type \[ \left\{\begin{array}{ll} -Δu = f(|x|, u) \qquad & \text{ in } Ω, \\ u= 0 & \text{ on } \partial Ω, \…
Asymptotic profile and Morse index of nodal radial solutions to the Hénon problem
Anna Lisa Amadori, Francesca Gladiali
We compute the Morse index of nodal radial solutions to the Hénon problem \[\left\{\begin{array}{ll} -Δu = |x|^α|u|^{p-1} u \qquad & \text{ in } B, \newline u= 0 & \text{ on } \par…
On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE's
Anna Lisa Amadori, Francesca Gladiali
We investigate nodal radial solutions to semilinear problems of type \[\begin{cases}-Δu = f(|x|,u) \qquad & \text{ in } Ω, \newline u= 0 & \text{ on } \partial Ω, \end{cases} \] wh…
Quasi-radial nodal solutions for the Lane-Emden problem in the ball
Francesca Gladiali, Isabella Ianni
We consider the semilinear elliptic problem \begin{equation}\label{problemAbstract} \left\{\begin{array}{lr}-Δu= |u|^{p-1}u\qquad \mbox{ in }B\\ u=0\qquad\qquad\qquad\mbox{ on }\pa…
Nonradial entire solutions for Liouville systems
Luca Battaglia, Francesca Gladiali, Massimo Grossi
We consider the following system of Liouville equations: $$\left\{\begin{array}{ll}-Δu_1=2e^{u_1}+μe^{u_2}&\text{in }\mathbb R^2\\-Δu_2=μe^{u_1}+2e^{u_2}&\text{in }\mathbb R^2\\\in…
Entire radial and nonradial solutions for systems with critical growth
Francesca Gladiali, Massimo Grossi, Christophe Troestler
In this paper we establish existence of radial and nonradial solutions to the system $$ \begin{array}{ll} -Δu_1 = F_1(u_1,u_2) &\text{in }\mathbb{R}^N,\newline -Δu_2 = F_2(u_1,u_2)…
Nonradial sign changing solutions to Lane Emden equation
Anna Lisa Amadori, Francesca Gladiali
In this paper we prove the existence of continua of nonradial solutions for the Lane-Emden equation. In a first result we show that there are infinitely many global continua detach…
Nodal solutions for Lane-Emden problems in almost-annular domains
Anna Lisa Amadori, Francesca Gladiali, Massimo Grossi
In this paper we prove an existence result to the problem w…
A non-variational system involving the critical Sobolev exponent. The radial case
Francesca Gladiali, Massimo Grossi, Christophe Troestler
In this paper we consider the non-variational system $$ \begin{cases} -Δu_i = \sum\limits_{j=1}^k a_{ij} u_j^{(N+2)/(N-2)} &\text{in }\mathbb R^N,\newline u_i>0 &\text{in }\mathbb…