Jarosław Mederski

activity

20132026

most citedNormalized ground states of the nonlinear Schrödinger equation with at least mass critical growth

103 citations · 301 across the 31 of their papers we have counts for

collaborators

Showing math.APShow all

41 papers · 1 filter

math.AP2026

Critical curl extremals and the hyperbolic plane

Jarosław Mederski

We study the critical Sobolev-curl quotient on $R^{3}$ at the conformally invariant exponent $p = 3/2$ . Its sharp constant and optimizers were posed as open problems in the li…

math.AP2026

Global well-posedness and orbital stability of the Gross--Pitaevskii branch in a coupled defocusing Schrödinger system

Michał Kowalczyk, Jarosław Mederski, Isidora Miranda

We consider a one-dimensional coupled defocusing Schrödinger system with a nonzero background in its first component and finite mass in its second component. We prove global well-p…

math.AP2026

On a critical curl-curl system of Lane-Emden type

Ioannis Arkoudis, Jarosław Mederski, Andrzej Szulkin

We study the system $\nabla \times \nabla \times u = ∣ v ∣^{q - 2} v$ , $\nabla \times \nabla \times v = ∣ u ∣^{p - 2} u$ of Lane-Emden type in $R^{3}$ , with exponents $p, q > 3$ on the critical…

math.AP2026

Explicit counterexamples to Frank-Loss optimizer conjectures for critical Dirac and vector Sobolev inequalities

Bartosz Bieganowski, Jarosław Mederski

Frank and Loss proposed critical Sobolev inequalities for the Dirac operator and for vector fields. They conjectured optimality of their spinorial family and wrote that it is conce…

math.AP2026

Ground state solutions to Born-Infeld-Choquard problem

Jarosław Mederski, Xiangjian Zeng

In this paper, we investigate the existence and qualitative properties of ground state solutions for the nonlocal Born-Infeld-Choquard problem \begin{equation*} \begin{cases} -{\rm…

math.AP2025

Ground state solutions to the nonlinear Born-Infeld problem

Bartosz Bieganowski, Norihisa Ikoma, Jarosław Mederski

In the paper we show the existence of ground state solutions to the nonlinear Born-Infeld problem \[ \mathrm{div}\, \left( \frac{\nabla u}{\sqrt{1-|\nabla u|^2}} \right) + f(u) = 0…

math.AP2025

Optimizers in Sobolev-curl inequalities

Jarosław Mederski, Andrzej Szulkin

We study a Sobolev-type inequality involving the $p$ -curl operator in $R^{3}$ . We prove the existence of a minimizer $u : R^{3} \to R^{3}$ which yields a solution…

math.AP2025

Polyharmonic Nonlinear Scalar Field Equations

Alessandro Cannone, Silvia Cingolani, Jarosław Mederski

In this paper, we present a result on the existence of ground state solutions for the polyharmonic nonlinear equation $(- Δ)^{m} u = g (u)$ , assuming that $g$ has a general subcritical g…

math.AP2024

Traveling waves for nonlinear Schrödinger equations

Laura Baldelli, Bartosz Bieganowski, Jarosław Mederski

We look for traveling wave solutions to the nonlinear Schrödinger equation with a subsonic speed, covering several physical models with Sobolev subcritical nonlinear effects. Our a…

math.AP2024

Travelling waves for Maxwell's equations in nonlinear and symmetric media

Jarosław Mederski, Jacopo Schino

We look for travelling wave fields $E (x, y, z, t) = U (x, y) cos (k z + ω t) + U (x, y) sin (k z + ω t), (x, y, z) \in R^{3}, t \in R,$ satisfying Maxwell's equations…

math.AP2024

Multiple normalized solutions to a system of nonlinear Schrödinger equations

Jarosław Mederski, Andrzej Szulkin

We find a normalized solution $u = (u_{1}, \dots, u_{K})$ to the system of $K$ coupled nonlinear Schrödinger equations \begin{equation*} \left\{ \begin{array}{l} -Δu_i+ λ_i u_i = \sum_{j=…

math.AP2024

Between Maxwell and Born-Infeld: the presence of the magnetic field

Pietro d'Avenia, Jarosław Mederski

Our motivation is to consider an electromagnetic Lagrangian density $L_{q}$ , depending on a parameter such that, for $q = 1$ it corresponds to the Born-Infeld Lagrangian dens…

math.AP2023

Normalized solutions to Born-Infeld and quasilinear problems

Laura Baldelli, Jarosław Mederski, Alessio Pomponio

The paper concerns the existence of normalized solutions to a large class of quasilinear problems, including the well-known Born-Infeld operator. In the mass subcritical cases, we…

math.AP2023

Semiclassical states for the curl-curl problem

Bartosz Bieganowski, Adam Konysz, Jarosław Mederski

We show the existence of the so-called semiclassical states $U : R^{3} \to R^{3}$ to the following curl-curl problem $$ \varepsilon^2\; \nabla \times (\nabla \ti…

math.AP2023★ 8 cited

Normalized solutions to Schrödinger equations in the strongly sublinear regime

Jarosław Mederski, Jacopo Schino

We look for solutions to the Schrödinger equation \[ -Δu + λu = g(u) \quad \text{in } \mathbb{R}^N \] coupled with the mass constraint $\int_{R^{N}} ∣ u ∣^{2} d x = ρ^{2}$ , with $N…

math.AP2022

Normalized solutions to at least mass critical problems: singular polyharmonic equations and related curl-curl problems

Bartosz Bieganowski, Jarosław Mederski, Jacopo Schino

We are interested in the existence of normalized solutions to the problem \begin{equation*} \begin{cases} (-Δ)^m u+\fracμ{|y|^{2m}}u + λu = g(u), \quad x = (y,z) \in \mathbb{R}^K \…

math.AP2021

Travelling waves for Maxwell's equations in nonlinear and nonsymmetric media

Jarosław Mederski, Wolfgang Reichel

We look for travelling wave fields $E (x, y, z, t) = U (x, y) cos (k z + ω t) + U (x, y) sin (k z + ω t), (x, y, z) \in R^{3}, t \in R$ satisfying Maxwell's equations…

math.AP2021

Born-Infeld problem with general nonlinearity

Jarosław Mederski, Alessio Pomponio

In this paper, using variational methods, we look for non-trivial solutions for the following problem $$ \begin{cases} -{\rm div}\left(a(|\nabla u|^2)\nabla u\right)=g(u), & \hbox{…

math.AP2021

Biharmonic nonlinear scalar field equations

Jarosław Mederski, Jakub Siemianowski

We prove a Brezis-Kato-type regularity result for weak solutions to the biharmonic nonlinear equation $Δ^{2} u = g (x, u) in R^{N}$ with a Carathéodory function $…

math.AP2021★ 1 cited

Nonlinear curl-curl problems in $R^{3}$

Jarosław Mederski, Jacopo Schino

We survey recent results concerning ground states and bound states $u : R^{3} \to R^{3}$ to the curl-curl problem $$\nabla\times(\nabla\times u)+V(x)u= f(x,u) \quad\…

math.AP2021★ 1 cited

Least energy solutions to a cooperative system of Schrödinger equations with prescribed $L^{2}$ -bounds: at least $L^{2}$ -critical growth

Jarosław Mederski, Jacopo Schino

We look for least energy solutions to the cooperative systems of coupled Schrödinger equations \begin{equation*} \begin{cases} -Δu_i + λ_i u_i = \partial_iG(u)\quad \mathrm{in} \ \…

math.AP2020★ 6 cited

Nonlinear scalar field equation with competing nonlocal terms

Pietro d'Avenia, Jarosław Mederski, Alessio Pomponio

We find radial and nonradial solutions to the following nonlocal problem $- Δ u + ω u = (I_{α} * F (u)) f (u) - (I_{β} * G (u)) g (u) in R^{N}$ under general a…

math.AP2020★ 7 cited

Multiple solutions to cylindrically symmetric curl-curl problems and related Schrödinger equations with singular potentials

Michał Gaczkowski, Jarosław Mederski, Jacopo Schino

We look for multiple solutions $U : R^{3} \to R^{3}$ to the curl-curl problem \[ \nabla\times\nabla\times\mathbf{U}=h(x,\mathbf{U}),\qquad x\in\mathbb{R}^3,…

math.AP2020★ 103 cited

Normalized ground states of the nonlinear Schrödinger equation with at least mass critical growth

Bartosz Bieganowski, Jarosław Mederski

We propose a simple minimization method to show the existence of least energy solutions to the normalized problem \begin{cases} -Δu + λu = g(u) \quad \mathrm{in} \ \mathbb{R}^N, \…

Critical curl extremals and the hyperbolic plane

Global well-posedness and orbital stability of the Gross--Pitaevskii branch in a coupled defocusing Schrödinger system

On a critical curl-curl system of Lane-Emden type

Explicit counterexamples to Frank-Loss optimizer conjectures for critical Dirac and vector Sobolev inequalities

Ground state solutions to Born-Infeld-Choquard problem

Ground state solutions to the nonlinear Born-Infeld problem

Optimizers in Sobolev-curl inequalities

Polyharmonic Nonlinear Scalar Field Equations

Traveling waves for nonlinear Schrödinger equations

Travelling waves for Maxwell's equations in nonlinear and symmetric media

Multiple normalized solutions to a system of nonlinear Schrödinger equations

Between Maxwell and Born-Infeld: the presence of the magnetic field

Normalized solutions to Born-Infeld and quasilinear problems

Semiclassical states for the curl-curl problem

Normalized solutions to Schrödinger equations in the strongly sublinear regime

Normalized solutions to at least mass critical problems: singular polyharmonic equations and related curl-curl problems

Travelling waves for Maxwell's equations in nonlinear and nonsymmetric media

Born-Infeld problem with general nonlinearity

Biharmonic nonlinear scalar field equations

Nonlinear curl-curl problems in R3

Least energy solutions to a cooperative system of Schrödinger equations with prescribed L2-bounds: at least L2-critical growth

Nonlinear scalar field equation with competing nonlocal terms

Multiple solutions to cylindrically symmetric curl-curl problems and related Schrödinger equations with singular potentials

Normalized ground states of the nonlinear Schrödinger equation with at least mass critical growth

Nonlinear curl-curl problems in $R^{3}$

Least energy solutions to a cooperative system of Schrödinger equations with prescribed $L^{2}$ -bounds: at least $L^{2}$ -critical growth