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arXiv · 2201.09705

Normalized solutions to a non-variational Schr\"odinger system

Mónica Clapp·Andrzej Szulkin
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Abstract

We establish the existence of positive normalized (in the $L^2$ sense) solutions to non-variational weakly coupled elliptic systems of $\ell$ equations. We consider couplings of both cooperative and competitive type. We show the problem can be formulated as an operator equation on the product of $\ell$ $L^2$-spheres and apply a degree-theoretical argument on this product to obtain existence.

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Mónica Clapp, Andrzej Szulkin. 2022-01-24. Normalized solutions to a non-variational Schr\"odinger system. https://arxiv.org/abs/2201.09705

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