Zobrazeno 1 - 10
of 126
pro vyhledávání: '"Mederski, Jarosław"'
We look for traveling wave solutions to the nonlinear Schr\"odinger equation with a subsonic speed, covering several physical models with Sobolev subcritical nonlinear effects. Our approach is based on a variant of Sobolev-type inequality involving t
Externí odkaz:
http://arxiv.org/abs/2406.03910
Autor:
Mederski, Jarosław, Schino, Jacopo
We look for travelling wave fields $$ E(x,y,z,t)= U(x,y) \cos(kz+\omega t)+ \widetilde U(x,y)\sin(kz+\omega t),\quad (x,y,z)\in\mathbb{R}^3,\, t\in\mathbb{R}, $$ satisfying Maxwell's equations in a nonlinear and cylindrically symmetric medium. We obt
Externí odkaz:
http://arxiv.org/abs/2406.01433
Autor:
Mederski, Jarosław, Szulkin, Andrzej
We find a normalized solution $u=(u_1,\ldots,u_K)$ to the system of $K$ coupled nonlinear Schr\"odinger equations \begin{equation*} \left\{ \begin{array}{l} -\Delta u_i+ \lambda_i u_i = \sum_{j=1}^K\beta_{i,j}u_i|u_i|^{p/2-2}|u_j|^{p/2} \quad \mathrm
Externí odkaz:
http://arxiv.org/abs/2403.16987
Autor:
d'Avenia, Pietro, Mederski, Jarosław
Our motivation is to consider an electromagnetic Lagrangian density $\mathcal{L}_q$, depending on a parameter such that, for $q=1$ it corresponds to the Born-Infeld Lagrangian density and for $q=2$ it restores the Maxwell one. The model in the presen
Externí odkaz:
http://arxiv.org/abs/2403.08924
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 study a global minimization problem and obtain a ground state solution
Externí odkaz:
http://arxiv.org/abs/2312.15025
We show the existence of the so-called semiclassical states $\mathbf{U}:\mathbb{R}^3\to\mathbb{R}^3$ to the following curl-curl problem $$ \varepsilon^2\; \nabla \times (\nabla \times \mathbf{U}) + V(x) \mathbf{U} = g(\mathbf{U}), $$ for sufficiently
Externí odkaz:
http://arxiv.org/abs/2312.03658
Autor:
Mederski, Jarosław, Schino, Jacopo
Publikováno v:
Calc. Var. Partial Differential Equations 63 (2024)
We look for solutions to the Schr\"odinger equation \[ -\Delta u + \lambda u = g(u) \quad \text{in } \mathbb{R}^N \] coupled with the mass constraint $\int_{\mathbb{R}^N}|u|^2\,dx = \rho^2$, with $N\ge2$. The behaviour of $g$ at the origin is allowed
Externí odkaz:
http://arxiv.org/abs/2306.06015
We are interested in the existence of normalized solutions to the problem \begin{equation*} \begin{cases} (-\Delta)^m u+\frac{\mu}{|y|^{2m}}u + \lambda u = g(u), \quad x = (y,z) \in \mathbb{R}^K \times \mathbb{R}^{N-K}, \\ \int_{\mathbb{R}^N} |u|^2 \
Externí odkaz:
http://arxiv.org/abs/2212.12361
Autor:
Mederski, Jarosław, Reichel, Wolfgang
We look for travelling wave fields $$ E(x,y,z,t)= U(x,y) \cos(kz+\omega t)+ \widetilde U(x,y)\sin(kz+\omega t),\quad (x,y,z)\in\mathbb{R}^3,\, t\in\mathbb{R} $$ satisfying Maxwell's equations in a nonlinear medium which is not necessarily cylindrical
Externí odkaz:
http://arxiv.org/abs/2112.15146
Autor:
Mederski, Jarosław, Pomponio, Alessio
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{in }\mathbb{R}^N,\; N\geq 3, \\[1mm] u(x)\to 0, &\hbox{as }|x|\to +\in
Externí odkaz:
http://arxiv.org/abs/2109.10155