Advances in Nonlinear Analysis (Jun 2018)

Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth

  • Cassani Daniele,
  • Zhang Jianjun

Journal volume & issue
Vol. 8, no. 1
pp. 1184 – 1212


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We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth in the sense of the Hardy–Littlewood–Sobolev inequality, in the range of the so-called upper-critical exponent. Qualitative behavior and concentration phenomena of solutions are also studied. Our approach turns out to be robust, as we do not require the nonlinearity to enjoy monotonicity nor Ambrosetti–Rabinowitz-type conditions, still using variational methods.