Normalized solutions to a non-variational Schrödinger system
DOI:
https://doi.org/10.12775/TMNA.2022.040Keywords
Morse index, Brouwer degree, weakly coupled elliptic system, positive solution, uniform boundAbstract
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.References
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