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Abstract
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We consider the positive solutions of some integral systems related to the static
Hartree-type equations:
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where
,
,
,
and
. Firstly, assuming
that the exponent
belongs to some suitable interval depending on the parameters
, we
are able to prove some nonexistence results for the positive solution. Secondly, we
also establish some qualitative results for the integrable solution of the system like
regularity, symmetry and asymptotic behaviour. As a corollary, we deduce the
corresponding results for the equivalent weighted Hartree-type nonlocal equations.
The results obtained in this paper generalise and complement the existing results in
the literature.
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Keywords
integral systems, weighted Hartree equation, Riesz
potential, integrable solution, decay rate
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Mathematical Subject Classification
Primary: 35J15
Secondary: 45G05
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Milestones
Received: 17 June 2021
Accepted: 17 March 2022
Published: 19 June 2022
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