Abstract
In this paper, we identify the sharp energy threshold for the global existence and blow-up to the Hartree equation with a focusing and defocusing perturbation, respectively, by utilizing comprehensive potential-well structures generated by the combined nonlinearities. Then, by adopting the refined compactness lemma, we detect the dynamical properties of blow-up solutions near the sharp threshold mass, including blow-up rate, concentration, weak limits and limiting profile decomposition of blow-up solutions with small super critical mass.
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