Hartree-Fock type systems: existence of ground states and asymptotic behavior

Abstract

In this paper we consider an Hartree-Fock type system made by two Schrödinger equations in presence of a Coulomb interacting term and a cooperative pure power and subcritical nonlinearity, driven by a suitable parameter $\beta \ge 0$. We show the existence of semitrivial and vectorial ground states solutions depending on the parameters involved. The asymptotic behavior with respect to the parameter $\beta$ of these solutions is also studied.

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