Superlinear Kirchhoff-type problems of the fractional p-Laplacian without the (AR) condition

Abstract

In this paper, we study the following superlinear p-Kirchhoff-type equation: $$\begin{aligned} \textstyle\begin{cases} \mathcal{M} (\int_{\mathbb{R}^{2N}}\frac { \vert u(x)-u(y) \vert ^{p}}{ \vert x-y \vert ^{N+ps}}\,dx\,dy )(-\triangle)^{s}_{p}u(x) -\lambda \vert u \vert ^{p-2}u=g(x,u)& \mbox{in }\varOmega,\\ u=0& \mbox{in }\mathbb{R}^{N}\backslash\varOmega, \end{cases}\displaystyle \end{aligned}$$ Under suitable assumptions on $g(x,u)$ without the (AR) condition, the existence of infinitely many solutions for the Kirchhoff equation of a fractional p-Laplacian is obtained by using the fountain theorem. Our conclusions generalize and extend some existing results.

Locations

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