Normalized solutions to a non-variational Schrödinger system - Clapp, Mónica; Szulkin, Andrzej (Topological Methods in Nonlinear Analysis, 2023)
We establish the existence of positive normalized (in the L^2 sense) solutions to non-variational weakly coupled elliptic systems of 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 L^2-spheres and apply a degree-theoretical argument on this product to obtain existence.