Nonlinear Choquard equations involving a critical local term

作者：Seok Jinmyoung^*

来源：Applied Mathematics Letters, 2017, 63: 77-87.

DOI：10.1016/j.aml.2016.07.027

• Semilinear elliptic
• Variational methods
• Hartree type nonlocal term
• Critical problem

We consider a critical version of nonlinear Choquard equation
{-Delta u + u = (I-alpha * vertical bar u vertical bar(p-2)u + lambda vertical bar u vertical bar(2)*(-2)u in R-N,
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u(x) = 0,
where I-alpha denotes the Riesz potential. This equation can be seen as a nonlocal perturbation of the usual critical problem in a whole space. Using some perturbation arguments, we construct a family of nontrivial solutions, which converges to a least energy solution of the limiting critical local problem as alpha -> 0.

• 出版日期2017-1