arXiv subjects

Sabrina Caputo

Publications and source records attributed to Sabrina Caputo.

3 recordsLinked to original sources

arXiv2026

Segregated solutions for a critical Choquard system with a small interspecies repulsive force

In this work, I focus on a coupled system of nonlinear Choquard equations in dimension 4, characterized by critical nonlocal nonlinearities and a small repulsive interspecies interaction. I prove the existence of a new class of multi-bubble segregated solutions. Specifically, I construct solutions where the first component concentrates as a radial positive ground state, while the second component exhibits a blow-up behaviour, concentrating at k points arranged as the vertices of a regular polygon. The proof relies on a sophisticated finite-dimensional reduction method, bridging the gap between the theory of competitive systems and critical nonlocal equations. My results show that the presence of nonlocal terms preserves the qualitative segregation patterns typically observed in local Schrodinger systems.

math.AP↗

arXiv2025

Infinitely many non-radial solutions to a critical Choquard equation

In this paper we study a class of critical Choquard equations with a symmetric potential, i.e. we consider the equation $$-\Delta u +V(|x|) u =\left(|x|^{-\mu}* |u|^{2^\star_\mu}\right)|u|^{2^\star_\mu-2}u,\quad\mbox{in}\quad\mathbb R^N$$ where $V(|x|)$ is a bounded, nonnegative and symmetric potential in $\mathbb R^N$ with $N\geq 5$, $0<\mu\leq 4$, $*$ stands for the standard convolution and $2^\star_\mu:=\frac{2N-\mu}{N-2}$ is the upper critical exponent in the sense of the Hardy - Littlewood - Sobolev inequality. By applying a finite dimensional reduction method we prove that if $r^2V(r)$ has a local maximum point or local minimum point $r_0>0$ with $V(r_0)>0$ then the problem has infinitely many non-radial solutions with arbitrary large energies.

math.AP↗

arXiv2024

Partially concentrating solutions for systems with Lotka-Volterra type interactions

In this paper we consider the existence of standing waves for a coupled system of $k$ equations with Lotka-Volterra type interaction. We prove the existence of a standing wave solution with all nontrivial components satisfying a prescribed asymptotic profile. In particular, the $k-1$-last components of such solution exhibits a concentrating behavior, while the first one keeps a quantum nature. We analyze first in detail the result with three equations since this is the first case in which the coupling has a role contrary to what happens when only two densities appear. We also discuss the existence of solutions of this form for systems with other kind of couplings making a comparison with Lotka-Volterra type systems.

math.AP↗