New existence of multiple solutions for nonhomogeneous Schrödinger–Kirchhoff problems involving the fractional p-Laplacian with sign-changing potential

Abstract

In this paper, we prove the existence of multiple solutions for the following fractional p-Laplacian equation of Schrodinger–Kirchhoff type with sign-changing potential $$\begin{aligned} M\left( \int \int _{{\mathbb {R}}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right) (-\Delta )^s_p u+V(x)|u|^{p-2}u=f(x,u)+ g(x),\quad x\in {\mathbb {R}}^N, \end{aligned}$$ where \((-\Delta )^s_p\) denotes the fractional p-Laplacian of order \(s\in (0,1)\), \(2\le p<\infty \), \(ps<N\), V(x) is allowed to be sign-changing and \(g : {\mathbb {R}}^N\rightarrow {\mathbb {R}}\) is a perturbation. Under some certain assumptions on f which is much weaker than those in Pucci et al. (Calc. Var. 54 : 2785-2806 2015), by using variation methods, we obtain infinitely many solutions for this equations. Our results generalize and extend some existing results.