In this paper, we deal with the multiplicity results for Kirchhoff equations with Hardy-Littlewood-Sobolev critical nonlinearity in \(\mathbb {R}^{N}\). By using the second concentration-compactness principle and concentration-compactness principle at infinity to prove that the (PS)_c condition holds locally and together with the new version of symmetric mountain pass theorem of Kajikiya, we prove that the problem admits infinitely many solutions under suitable conditions.

中文翻译：

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具有Hardy-Littlewood-Sobolev临界非线性的Kirchhoff方程的多重结果

在本文中，我们用\（\ mathbb {R} ^ {N} \）中的Hardy-Littlewood-Sobolev临界非线性处理Kirchhoff方程的多重结果。通过使用无穷大处的第二个浓度紧致原理和浓度紧致原理，证明了（P S）_c条件是局部成立的，并结合了Kajikiya的新版对称山pass定理，我们证明了该问题允许无数个解在合适的条件下。