Analysis demonstrates existence of standing waves in a quantum system, suggesting new insights into nonlinear effects.
We study standing waves of the Schrödinger equation with constant magnetic field and combined power nonlinearities, which describes a single non‐relativistic quantum particle in the presence of an electromagnetic field. We develop the local minima geometry method to establish the existence, estimates and mass collapse results for this equation, which generalize exiting results in the literature.
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Feng et al. (2025) studied this question.
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