Nodal solutions for pseudo-relativistic Hartree equations
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DOI: 10.1016/j.jmaa.2020.124474
Abstract: Abstract In this paper, we investigate the existence of nodal solutions for the following problem where 1 2 α 1 , 0 μ ≤ 2 and 2 N − μ N − 1 p 2… read more here.
Keywords: hartree equations; nodal solutions; relativistic hartree; pseudo relativistic ... See more keywords
Uniqueness of ground states for nonlinear Hartree equations
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DOI: 10.1063/1.5051026
Abstract: We consider ground states of nonlinear Hartree equations with trapping potentials V(x), which can be described equivalently by positive minimizers of L2-critical Hartree energy functional. It is known that ground states exist if and only… read more here.
Keywords: hartree equations; ground; uniqueness ground; states nonlinear ... See more keywords
On well-posedness for inhomogeneous Hartree equations in the critical case
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DOI: 10.3934/cpaa.2023060
Abstract: We study the well-posedness for the inhomogeneous Hartree equation $i\partial_t u + \Delta u = \lambda(I_\alpha \ast |\cdot|^{-b}|u|^p)|x|^{-b}|u|^{p-2}u$ in $H^s$, $s\ge0$. Until recently, its well-posedness theory has been intensively studied, focusing on solving the problem… read more here.
Keywords: inhomogeneous hartree; hartree equations; critical case; case ... See more keywords
The well-posedness and convergence of higher-order Hartree equations in critical Sobolev spaces on $ \mathbb{T}^3 $
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DOI: 10.3934/dcds.2025145
Abstract: In this article, we consider Hartree equations generalised to $2p+1$ order nonlinearities. These equations arise in the study of the mean-field limits of Bose gases with $p$-body interactions. We study their well-posedness properties in $H^{s_c}(\mathbb{T}^3)$,… read more here.
Keywords: higher order; hartree equations; well posedness; order hartree ... See more keywords