Demonstrates the existence of single-peak solutions in the critical Hartree equation with electromagnetic field, highlighting theoretical implications.
In this paper, we study the following critical Hartree equation with electromagnetic field [Formula: see text] where [Formula: see text] is the imaginary unit, [Formula: see text] is the upper critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality, [Formula: see text] [Formula: see text], [Formula: see text] and [Formula: see text] is a small parameter. The magnetic potential [Formula: see text] is a bounded real-valued vector field on [Formula: see text] and [Formula: see text] denotes an electric potential. Under some suitable assumptions on [Formula: see text] and [Formula: see text], we establish the existence of single-peak solutions by applying the finite-dimensional reduction argument within the framework of critical point theory.
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Chen et al. (2026) studied this question.
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