[PDF] Least energy solutions to a cooperative system of Schr\"odinger equations with prescribed $L^2$-bounds: at least $L^2$-critical growth | Semantic Scholar

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Corpus ID: 230799621

Least energy solutions to a cooperative system of Schr\"odinger equations with prescribed $L^2$-bounds: at least $L^2$-critical growth

@inproceedings{Mederski2021LeastES,
title={Least energy solutions to a cooperative system of Schr\"odinger equations with prescribed \$L^2\$-bounds: at least \$L^2\$-critical growth},
author={Jaroslaw Mederski and Jacopo Schino},
year={2021}
}

with G ≥ 0, where ρi > 0 is prescribed and (λi, ui) ∈ R × H(R ) is to be determined, i ∈ {1, . . . ,K}. Our approach is based on the minimization of the energy functional over a linear combination of the Nehari and Pohožaev constraints intersected with the product of the closed balls in L(R ) of radii ρi, which allows to provide general growth assumptions on G and to know in advance the sign of the corresponding Lagrange multipliers. We assume that G has at least L-critical growth at 0 and… CONTINUE READING