#### Jiabin Zuo, Tianqing An, Xiuzhen Li, Yanying Ma, A fractional p-Kirchhoff type problem involving a parameter, Vol. 2019 (2019), Article ID 32, pp. 1-14

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DOI: 10.23952/jnfa.2019.32

Received April 17, 2019; Accepted July 14, 2019; Published July 26, 2019

Abstract. In this paper, by using the symmetric mountain pass theorem and dual fountain theorem, we show the existence of infinitely many solutions for the nonlocal Kirchhoff type equation with the fractional p-Laplacian:

$p\mathcal{M}\Big{(}\iint_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+ps}}dxdy\Big{)} (-\triangle)^{s}_{p}u(x)-\lambda|u|^{p-2}u=f(x,u),$  in $\Omega,$

$u=0,$ in $\mathbb{R}^{N}\backslash\Omega,$

where $\Omega\subset\mathbb{R}^{N}$ is a smooth bounded domain, $(-\triangle)^{s}_{p}$ is a fractional p-Laplace operator with $0 and $ps, $\mathcal{M}$ is a continuous function and $\lambda$ is a real parameter.