Bartosz Bieganowski

collaborators

5 papers

math.AP2018

Schrödinger-type equations with sign-changing nonlinearities: a survey

Bartosz Bieganowski

We are looking for solutions to nonlinear Schrödinger-type equations of the form $(- Δ)^{α /2} u (x) + V (x) u (x) = h (x, u (x)), x \in R^{N},$ where $V : \mathbb{R}^N…

math.AP2018

Note on semiclassical states for the Schrödinger equation with nonautonomous nonlinearities

Bartosz Bieganowski, Jarosław Mederski

We consider the following Schrödinger equation $- ℏ^{2} Δ u + V (x) u = Γ (x) f (u) in R^{N},$ where $u \in H^{1} (R^{N})$ , $u > 0$ , $ℏ > 0$ …

math.AP2018

The semirelativistic Choquard equation with a local nonlinear term

Bartosz Bieganowski, Simone Secchi

We propose an existence result for the semirelativistic Choquard equation with a local nonlinearity in $R^{N}$ \begin{equation*} \sqrt{\strut -Δ+ m^2} u - mu + V(x)u = \left…

math.AP2018

Systems of coupled Schrödinger equations with sign-changing nonlinearities via classical Nehari manifold approach

Bartosz Bieganowski

We propose existence and multiplicity results for the system of Schrödinger equations with sign-changing nonlinearities in bounded domains or in the whole space $R^{N}$ . In…

math.AP2018

The fractional Schrödinger equation with Hardy-type potentials and sign-changing nonlinearities

Bartosz Bieganowski

We look for solutions to a fractional Schrödinger equation of the following form $$ (-Δ)^{α/ 2} u + \left( V(x) - \fracμ{|x|^α} \right) u = f(x,u)-K(x)|u|^{q-2}u\hbox{ on }\mathbb{…