arXiv subjects

Andrea Sfecci

Publications and source records attributed to Andrea Sfecci.

8 recordsLinked to original sources

arXiv2024

A bifurcation phenomenon for the critical Laplace and $p$-Laplace equation in the ball

In this paper we show that the number of radial positive solutions of the following critical problem $$ \Delta_p u(x) + \lambda K(|x|) \,u(x) \, |u(x)|^{q-2} =0\,,$$ $$ u(x)>0 \quad |x|<1,$$ $$ u(x)=0 \quad |x|=1,$$ where $q= \frac{np}{n-p}$, $\frac{2n}{n+2} \le p \le 2$ and $x \in \mathbb{R}^n$, undergoes a bifurcation phenomenon. Namely, the problem admits one solution for any $\lambda>0$ if $K$ is steep enough at $0$, while it admits no solutions for $\lambda$ small and two solutions for $\lambda$ large if $K$ is too flat at $0$. The existence of the second solution is new, even in the classical Laplace case. The proofs use Fowler transformation and dynamical systems tools.

math.AP↗

arXiv2024

A Poincar\'e-Birkhoff theorem for multivalued successor maps with applications to periodic superlinear Hamiltonian systems

We provide a new version of the Poincar\'e-Birkhoff theorem for possibly multivalued successor maps associated with planar non-autonomous Hamiltonian systems. As an application, we prove the existence of periodic and subharmonic solutions of the scalar second order equation $\ddot x + \lambda g(t,x) = 0$, for $\lambda>0$ sufficiently small, with $g(t,x)$ having a superlinear growth at infinity, without requiring the existence of an equilibrium point.

math.CA↗

arXiv2018

Double resonance in Sturm-Liouville planar boundary value problems

We provide some existence results for Sturm-Liouville boundary value problems associated with the planar differential system $Jz' = g(t, z) + r(t, z)$ where g is suitably controlled by the gradient of two positively homogeneous functions of degree 2 and r is bounded. We study the existence of solutions when a double resonance phenomenon occurs by the introduction of Landesman-Lazer type of conditions. Applications to scalar second order differential equations are given.

math.DS↗

arXiv2017

On the structure of radial solutions for some quasilinear elliptic equations

In this paper we study entire radial solutions for the quasilinear $p$-Laplace equation $Δ_p u + k(x) f(u) = 0$ where $k$ is a radial positive weight and the nonlinearity behaves e.g. as $f(u)=u|u|^{q-2}-u|u|^{Q-2}$ with $q<Q$. In particular we focus our attention on solutions (positive and sign changing) which are infinitesimal at infinity, thus providing an extension of a previous result by Tang (2001).

math.AP↗

arXiv2016

Entire solutions of superlinear problems with indefinite weights and Hardy potentials

We provide the structure of regular/singular fast/slow decay radially symmetric solutions for a class of superlinear elliptic equations with an in- definite weight on the nonlinearity f (u, r). In particular we are interested in the case where f is positive in a ball and negative outside, or in the re- versed situation. We extend the approach to elliptic equations in presence of Hardy potentials. By the use of Fowler transformation we study the corresponding dynamical systems, presenting the construction of invariant manifolds when the global existence of solutions is not ensured.

math.AP↗

arXiv2016

On a diffusion model with absorption and production

We discuss the structure of radial solutions of some superlinear elliptic equations which model diffusion phenomena when both absorption and production are present. We focus our attention on solutions defined in R (regular) or in R \ {0} (singular) which are infinitesimal at infinity, discussing also their asymptotic behavior. The phenomena we find are present only if absorption and production coexist, i.e., if the reaction term changes sign. Our results are then generalized to include the case where Hardy potentials are considered.

math.DS↗

arXiv2015

Double resonance for one-sided superlinear or singular nonlinearities

We deal with the problem of existence of periodic solutions for the scalar differential equation x" + f (t, x) = 0 when the asymmetric nonlinearity satisfies a one-sided superlinear growth at infinity. The nonlinearity is asked to be next to resonance and a Landesman-Lazer type of condition will be introduced in order to obtain a positive answer. Moreover we provide also the corresponding result for equations with a singularity and asymptotically linear growth at infinity, showing a further application to radially symmetric systems.

math.CA↗

arXiv2015

Periodic impact motions at resonance of a particle bouncing on spheres and cylinders

We investigate the existence of periodic trajectories of a particle, subject to a central force, which can hit a sphere, or a cylinder. We will provide also a Landesman-Lazer type of condition in the case of a nonlinearity satisfying a double resonance condition. Afterwards, we will show how such a result can be adapted to obtain a new result for the impact oscillator at double resonance.

math.CA↗