Adam Konysz

activity

20222026

collaborators

4 papers

math.AP2026

Nonlinear Schrödinger equations with a critical, inverse-square potential

Bartosz Bieganowski, Adam Konysz, Simone Secchi

We study the existence of solutions of the following nonlinear Schrödinger equation $- Δ u + V (x) u - \frac{( N - 2 ) ^{2}}{4∣ x ∣ ^{2}} u = f (x, u)$ where $V : R^{N} \to R$ and $f:\mathb…

math.AP2025

Note on elliptic equations on closed manifolds with singular nonlinearities

Bartosz Bieganowski, Adam Konysz

We consider a general elliptic equation $- Δ_{g} u + V (x) u = f (x, u) + g (x, u^{2}) u$ on a closed Riemannian manifold $(M, g)$ and utilize a recent variational approach by Hebey, Pacard, Pol…

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.AP2022

Elliptic problems with mixed nonlinearities and potentials singular at the origin and at the boundary of the domain

Bartosz Bieganowski, Adam Konysz

We are interested in the following Dirichlet problem $$ \left\{ \begin{array}{ll} -Δu + λu - μ\frac{u}{|x|^2} - ν\frac{u}{\mathrm{dist}\,(x,\mathbb{R}^N \setminus Ω)^2} = f(x,u) &…