8 papers
Normalized solutions to a non-variational Schrödinger system
Mónica Clapp, Andrzej Szulkin
We establish the existence of positive normalized (in the sense) solutions to non-variational weakly coupled elliptic systems of equations. We consider couplings of bo…
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…
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…
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…
Multiple solutions to a nonlinear curl-curl problem in
Jarosław Mederski, Jacopo Schino, Andrzej Szulkin
We look for ground states and bound states to the curl-curl problem which ori…
On some weakly coercive quasilinear problems with forcing
Andrzej Szulkin, Michel Willem
We consider the forced problem , where is the -Laplacian () in a domain , and $Q_V (u) := \int…