32 citations · 56 across the 8 of their papers we have counts for
4 papers · 1 filter
Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions
Filip Ficek
Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach bas…
Nonlinear Schrödinger equations with trapping potentials in higher dimensions
Filip Ficek
From the mathematical side, nonlinear Schrödinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome…
Schrödinger-Newton-Hooke system in higher dimensions. Part I: Stationary states
Filip Ficek
The Schrödinger equation with a harmonic potential coupled to the Poisson equation, called the Schrödinger-Newton-Hooke (SNH) system, has been considered in a variety of physical c…
Ground state in the energy super-critical Gross-Pitaevskii equation with a harmonic potential
Piotr Bizon, Filip Ficek, Dmitry E. Pelinovsky +1
The energy super-critical Gross--Pitaevskii equation with a harmonic potential is revisited in the particular case of cubic focusing nonlinearity and dimension d > 4. In order to p…