Abstract
This work deals with the existence of solutions for a class of Hartree–Fock type system in the two dimensional Euclidean space. Our approach is variational and based on a minimization technique in the Nehari manifold. The main steps in the prove are some trick estimates from the sign-changing logarithm potential in an appropriate subspace of \(H^1({\mathbb {R}}^2)\) introduced by Stubbe [23] (see also Cingolani-Weth [8]).
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The first author was supported by CAPES/BRAZIL.
The second author was supported by CNPq/BRAZIL and FAPDF.
The third author was supported by CNPq.
The last author was partially suppoted by Grant 2019/2014 Paraíba State Research Foundation (FAPESQ), FAPDF and CNPq 308900/2019-7.
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Carvalho, J., Figueiredo, G., Maia, L. et al. On a planar Hartree–Fock type system. Nonlinear Differ. Equ. Appl. 29, 56 (2022). https://doi.org/10.1007/s00030-022-00788-x
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DOI: https://doi.org/10.1007/s00030-022-00788-x