Nonlinear Choquard equations involving a critical local term

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• 作者：Jinmyoung Seok ^{jmseok@kgu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Semilinear elliptic ; Variational methods ; Hartree type nonlocal term ; Critical problem
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：63
• 期：Complete
• 页码：77-87
• 全文大小：616 K

文摘

We consider a critical version of nonlinear Choquard equation where acf03c89bb86c557eb" title="Click to view the MathML source">I_α$I_{\alpha }$ 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 α→0$\alpha \to 0$.