A. Szulkin

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math.AP2025

A concentration phenomenon for a semilinear SchrÃ¶dinger equation with periodic self-focusing core

MÃ³nica Clapp, Alberto SaldaÃ±a, Andrzej Szulkin

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

math.AP2025

Multiple normalized solutions to a system of nonlinear SchrÃ¶dinger equations

JarosÅaw Mederski, Andrzej Szulkin

We find a normalized solution $u = (u_{1}, \dots, u_{K})$ to the system of $K$ coupled nonlinear SchrÃ¶dinger equations \begin{equation*} \left\{ \begin{array}{l} -Îu_i+ Î»_i u_i = \sum_…

math.AP2024

On a SchrÃ¶dinger system with shrinking regions of attraction

MÃ³nica Clapp, Alberto SaldaÃ±a, 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…