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Original Articles

Behavior around isolated singularity for integral inequalities with multiple Riesz potentials

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Pages 1170-1182 | Received 18 Sep 2018, Accepted 18 Nov 2018, Published online: 12 Dec 2018

References

  • Chen W, Li C, Ou B. Classification of solutions for a system of integral equations. Commun Part Diff Equ. 2005;30:59–65. doi: 10.1081/PDE-200044445
  • Chen W, Li C, Ou B. Qualitative properties of solutions for an integral equation. Discrete Contin Dyn Syst. 2005;12:347–354.
  • Chen W, Li C, Ou B. Classification of solutions for an integral equation. Commun Pure Appl Math. 2006;59:330–343. doi: 10.1002/cpa.20116
  • Li YY. Remark on some conformally invariant integral equations: the method of moving spheres. J Eur Math Soc. 2004;6:153–180. doi: 10.4171/JEMS/6
  • Liu Y. A new method for converting boundary value problems for impulsive fractional differential equations to integral equations and its applications. Adv Nonlinear Anal., in press. Available from: https://doi.org/10.1515/anona-2016-0064
  • Villavert J. Qualitative properties of solutions for an integral system related to the Hardy–Sobolev inequality. J Diff Equ. 2015;258:1685–1714. doi: 10.1016/j.jde.2014.11.011
  • Frank F, Lieb E. Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality. Calc Var Part Diff Equ. 2010;39:85–99. doi: 10.1007/s00526-009-0302-x
  • Lieb E. Sharp constants in the Hardy–Littlewood–Sobolev and related inequalities. Ann Math. 1983;118:349–374. doi: 10.2307/2007032
  • Ghergu M, Taliaferro SD. Pointwise bounds and blow-up for Choquard–Pekar inequalities at an isolated singularity. J Diff Equ. 2016;261:189–217. doi: 10.1016/j.jde.2016.03.004
  • Cassani D, Zhang J. Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth. Adv Nonlinear Anal., in press. Available from: https://doi.org/10.1515/anona-2018-0019
  • Ghergu M, Kim S, Shahgholian H. Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity. Adv Nonlinear Anal., in press. Available from: https://doi.org/10.1515/anona-2017-0261
  • Singh G. Nonlocal perturbations of the fractional Choquard equation. Adv Nonlinear Anal., in press. Available from: https://doi.org/10.1515/anona-2017-0126
  • Taliaferro SD. Initial pointwise bounds and blow-up for parabolic Choquard–Pekar inequalities. Discrete Contin Dyn Syst. 2017;37:5211–5252. doi: 10.3934/dcds.2017226
  • Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. 2nd ed. Berlin: Springer-Verlag; 1983.
  • Brezis B, Lions PL. A note on isolated singularities for linear elliptic equations. Mathematical analysis and applications, Part A, Advances in Mathematics: Supplementary Studies. New York, London: Academic Press; 1981. p. 263–266.
  • Ghergu M, Taliaferro SD. Isolated singularities in partial differential inequalities. Cambridge (UK): Cambridge University Press; 2016.
  • Ghergu M, Taliaferro SD. Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities. Calc Var Part Diff Equ. 2015;54:1243–1273. doi: 10.1007/s00526-015-0824-3

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