A. Szulkin

activity

20122026

most citedA simple variational approach to weakly coupled competitive elliptic systems

39 citations · 98 across the 17 of their papers we have counts for

collaborators

21 papers

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.AP2025

A concentration phenomenon for a semilinear Schrödinger equation with periodic self-focusing core

Mónica Clapp, Alberto Saldaña, Andrzej Szulkin

We consider the equation $- Δ u + u = Q_{ε} (x) ∣ u ∣^{p - 2} u, u \in H^{1} (R^{N}),$ where $Q_{ε}$ takes the value $1$ on each ball $B_{ε} (y)$ , $y\in\mathbb…

math.AP2024

On a Schrödinger system with shrinking regions of attraction

Mónica Clapp, Alberto Saldaña, Andrzej Szulkin

In this paper we consider a competitive weakly coupled elliptic system in which each species is attracted to a small region and repelled from its complement. In this setting, we es…

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.AP2023

Configuration spaces and multiple positive solutions to a singularly perturbed elliptic system

Mónica Clapp, Alberto Saldaña, Andrzej Szulkin

We consider a weakly coupled singularly perturbed variational elliptic system in a bounded smooth domain with Dirichlet boundary conditions. We show that, in the competitive regime…

math.AP2022

Normalized solutions to a non-variational Schrödinger system

Mónica Clapp, Andrzej Szulkin

We establish the existence of positive normalized (in the $L^{2}$ sense) solutions to non-variational weakly coupled elliptic systems of $ℓ$ equations. We consider couplings of bo…

math.AP2021★ 3 cited

Non-variational weakly coupled elliptic systems

Mónica Clapp, Andrzej Szulkin

We establish the existence of a nonnegative fully nontrivial solution to a non-variational weakly coupled competitive elliptic system. We show that this kind of solutions belong to…

math.AP2020

Solutions to indefinite weakly coupled cooperative elliptic systems

Mónica Clapp, Andrzej Szulkin

We study the elliptic system \begin{equation*} \begin{cases} -Δu_1 - κ_1u_1 = μ_1|u_1|^{p-2}u_1 + λα|u_1|^{α-2}|u_2|^βu_1, \\ -Δu_2 - κ_2u_2 = μ_2|u_2|^{p-2}u_2 + λβ|u_1|^α|u_2|^{β…

math.AP2020★ 11 cited

A Sobolev-type inequality for the curl operator and ground states for the curl-curl equation with critical Sobolev exponent

Jarosław Mederski, Andrzej Szulkin

Let $Ω \subset R^{3}$ be a Lipschitz domain and let $S_{curl} (Ω)$ be the largest constant such that $$ \int_{\mathbb{R}^3}|\nabla\times u|^2\, dx\geq S_{\mathrm{curl}}…

math.AP2019

Phase separation, optimal partitions, and nodal solutions to the Yamabe equation on the sphere

Mónica Clapp, Alberto Saldaña, Andrzej Szulkin

We study an optimal M-partition problem for the Yamabe equation on the round sphere, in the presence of some particular symmetries. We show that there is a correspondence between s…

math.AP2019★ 39 cited

A simple variational approach to weakly coupled competitive elliptic systems

Mónica Clapp, Andrzej Szulkin

The main purpose of this paper is to exhibit a simple variational setting for finding fully nontrivial solutions to the weakly coupled elliptic system (1.1). We show that such solu…

math.AP2019★ 22 cited

Multiple solutions to a nonlinear curl-curl problem in $R^{3}$

Jarosław Mederski, Jacopo Schino, Andrzej Szulkin

We look for ground states and bound states $E : R^{3} \to R^{3}$ to the curl-curl problem $\nabla \times (\nabla \times E) = f (x, E) in R^{3}$ which ori…

math.AP2017

On some weakly coercive quasilinear problems with forcing

Andrzej Szulkin, Michel Willem

We consider the forced problem $- Δ_{p} u - V (x) ∣ u ∣^{p - 2} u = f (x)$ , where $Δ_{p}$ is the $p$ -Laplacian ( $1 < p < \infty$ ) in a domain $Ω \subset R^{N}$ , $V \geq 0$ and $Q_V (u) := \int…

math.AP2016

Generalized Nehari manifold and semilinear Schrödinger equation with weak monotonicity condition on the nonlinear term

Francisco Odair de Paiva, Wojciech Kryszewski, Andrzej Szulkin

We study the Schrödinger equations $- Δ u + V (x) u = f (x, u)$ in $R^{N}$ and $- Δ u - λ u = f (x, u)$ in a bounded domain $Ω \subset R^{N}$ . We assume that $f$ is superlinear bu…

math.AP2015★ 1 cited

A logarithmic Schrödinger equation with asymptotic conditions on the potential

Chao Ji, Andrzej Szulkin

In this paper we consider a class of logarithmic Schrödinger equations with a potential which may change sign. When the potential is coercive, we obtain infinitely many solutions b…

math.AP2015

Ground states of critical and supercritical problems of Brezis-Nirenberg type

Mónica Clapp, Angela Pistoia, Andrzej Szulkin

We study the existence of symmetric ground states to the supercritical problem \[ -Δv=λv+\left\vert v\right\vert ^{p-2}v\text{ \ in }Ω,\qquad v=0\text{ on }\partialΩ, \] in a domai…

math.AP2014

Bifurcation from infinity for an asymptotically linear Schrödinger equation

Wojciech Kryszewski, Andrzej Szulkin

We consider an asymptotically linear Schrödinger equation $- Δ u + V (x) u = λ u + f (x, u), x \in R^{N}$ , and show that if $λ_{0}$ is an isolated eigenvalue for the linearization at infinit…

math.AP2014★ 5 cited

Multiple solutions to logarithmic Schrodinger equations with periodic potential

Marco Squassina, Andrzej Szulkin

We study a class of logarithmic Schrodinger equations with periodic potential which come from physically relevant situations and obtain the existence of infinitely many geometrical…

math.AP2013

A supercritical elliptic problem in a cylindrical shell

Mónica Clapp, Andrzej Szulkin

We consider the problem \[ -Δu=|u|^{p-2}u in Ω, u=0 on \partialΩ, \] where $Ω := {(y, z) \in R^{m + 1} \times R^{N - m - 1} : 0 < a < ∣ y ∣ < b < \infty}$ , $0 \leq m \leq N - 1$ and $N\geq…

math.AP2012

Multiple solutions to nonlinear Schrödinger equations with singular electromagnetic potential

Mónica Clapp, Andrzej Szulkin

We consider the semilinear electromagnetic Schrödinger equation (-i\nabla+A(x))^{2}u + V(x)u = |u|^{2^{\ast}-2}u, u\in D_{A,0}^{1,2}(Ω,\mathbb{C}), where $Ω=(\mathbb{R}^{m}\smallse…

math.AP2012★ 17 cited

A concentration phenomenon for semilinear elliptic equations

Nils Ackermann, Andrzej Szulkin

For a domain $Ω\subset\dR^N$ we consider the equation $ -Δu + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p \in (2, 2^{*})$ . Here $V \geq 0$ and $Q_{n}$ are b…

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

A concentration phenomenon for a semilinear Schrödinger equation with periodic self-focusing core

On a Schrödinger system with shrinking regions of attraction

Multiple normalized solutions to a system of nonlinear Schrödinger equations

Configuration spaces and multiple positive solutions to a singularly perturbed elliptic system

Normalized solutions to a non-variational Schrödinger system

Non-variational weakly coupled elliptic systems

Solutions to indefinite weakly coupled cooperative elliptic systems

A Sobolev-type inequality for the curl operator and ground states for the curl-curl equation with critical Sobolev exponent

Phase separation, optimal partitions, and nodal solutions to the Yamabe equation on the sphere

A simple variational approach to weakly coupled competitive elliptic systems

Multiple solutions to a nonlinear curl-curl problem in R3

On some weakly coercive quasilinear problems with forcing

Generalized Nehari manifold and semilinear Schrödinger equation with weak monotonicity condition on the nonlinear term

A logarithmic Schrödinger equation with asymptotic conditions on the potential

Ground states of critical and supercritical problems of Brezis-Nirenberg type

Bifurcation from infinity for an asymptotically linear Schrödinger equation

Multiple solutions to logarithmic Schrodinger equations with periodic potential

A supercritical elliptic problem in a cylindrical shell

Multiple solutions to nonlinear Schrödinger equations with singular electromagnetic potential

A concentration phenomenon for semilinear elliptic equations

Multiple solutions to a nonlinear curl-curl problem in $R^{3}$