M. Rastrelli

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math.AP2026

Standing waves for defocusing nonlinear SchrÃ¶dinger equations with point interaction

Noriyoshi Fukaya, Yuki Osada, Mario Rastrelli

We consider standing waves of the nonlinear SchrÃ¶dinger equation $i \partial_{t} u = - I^_{I^} \pm u + ∣ u ∣^{p - 1} u$ in the defocusing case in dimensions $N = 2$ and $N = 3$ . Here, $- I^_{I^} \pm$ denote…

math.AP2025

Fractional Sobolev Spaces for the Singular-perturbed Laplace Operator in the $L^{p}$ setting

Vladimir Georgiev, Mario Rastrelli

We study the perturbed Sobolev spaces $H_{I^}^{s, p} \pm (R^{d})$ , associated with singular perturbation $I^_{I^} \pm$ of Laplace operator in Euclidean space of dimensions 2 and 3. We e…

math.AP2025

On the Cauchy problem for the reaction-diffusion system with point-interaction in $R^{2}$

Daniele Barbera, Vladimir Georgiev, Mario Rastrelli

The paper studies the existence of solutions for the reaction-diffusion equation in $R^{2}$ with point-interaction laplacian $I^_{I^} \pm$ with $I^\pm \in (- \infty, + \infty]$ , assuming t…

Standing waves for defocusing nonlinear SchrÃ¶dinger equations with point interaction

Fractional Sobolev Spaces for the Singular-perturbed Laplace Operator in the Lp setting

On the Cauchy problem for the reaction-diffusion system with point-interaction in R2

Fractional Sobolev Spaces for the Singular-perturbed Laplace Operator in the $L^{p}$ setting

On the Cauchy problem for the reaction-diffusion system with point-interaction in $R^{2}$