In this paper, we consider the following new Kirchhoff-type equations involving the fractional p-Laplacian and Hardy-Littlewood-Sobolev critical nonlinearity:

where (−Δ) ^p_s is the fractional p-Laplacian with 0 < s < 1 < p, 0 < μ < N, N > ps, a, b > 0, λ > 0 is a parameter, V: ℝ^N → ℝ⁺ is a potential function, θ ∈ [1, 2 ^*_μ,s ) and \(^{p_{\mu,s}^ * = {{pN - p{\mu \over 2}} \over {N - ps}}}\) is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. We get the existence of infinitely many solutions for the above problem by using the concentration compactness principle and Krasnoselskii’s genus theory. To the best of our knowledge, our result is new even in Choquard-Kirchhoff-type equations involving the p-Laplacian case.

在本文中，我们考虑以下涉及分数p -Laplacian 和 Hardy-Littlewood-Sobolev 临界非线性的新 Kirchhoff 型方程：

其中 (−Δ) ^p _s是分数p -拉普拉斯算子，其中 0 < s < 1 < p , 0 < μ < N, N > ps, a, b > 0, λ > 0 是一个参数，V : ℝ ^N → ℝ ⁺是一个势函数，θ ∈ [1, 2 ^* _μ,s ) 和\(^{p_{\mu,s}^ * = {{pN - p{\mu \over 2}} \over {N - ps}}}\) 是 Hardy-Littlewood-Sobolev 不等式意义上的临界指数。利用浓度紧致原理和Krasnoselskii的属理论，我们得到了上述问题的无穷多解的存在性。据我们所知，即使在涉及p -Laplacian 情况的 Choquard-Kirchhoff 型方程中，我们的结果也是新的。