Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 45, Issue 1, Pages 388-406Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120879282
Keywords
Hartree equation; Riesz potential; Liouville theorem; integrable solution; finite energy solution; decay rate
Categories
Funding
- NSF of China [11171158]
- Natural Science Foundation of Jiangsu [BK2012846]
- SRF for ROCS, SEM
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This paper is concerned with the positive solutions of a class of static Hartree-type equations. We translate these equations to the equivalent integral systems involving the Riesz potentials. Using the regularity lifting lemma by contracting operators, we obtain the integrability result for the integrable solution u of integral systems. Based on this result, we prove that the integrable solution decays quickly and the nonintegrable bounded solution decays almost slowly. Applying the equivalence, we finally give the corresponding results of the positive solutions of the Hartree-type equations.
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