Infinitely many solutions for a new class of Schrödinger–Kirchhoff type equations in $$\mathbb R^N$$ involving the fractional p-Laplacian

This paper deals with the existence of infinitely many solutions for a new class of Schrodinger–Kirchhoff type equations of the form $$\begin{aligned} M\left( [u]_{s,p}^p+\int _{\mathbb R^N}V(x)|u|^p\,dx\right) \left[ (-\Delta )_{p}^s u + V(x)|u|^{p-2}u\right] = \lambda h(x)|u|^{q-2}u + f(x,u), \; x\in \mathbb R^N, \end{aligned}$$ where $$\begin{aligned}{}[u]_{s,p}^p := \iint _{\mathbb R^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{ N+sp}}\,dx\,dy, \end{aligned}$$ $$s\in (0,1)$$ , $$N>sp$$ , $$p\ge 2$$ , $$M(t) = a -bt^{\gamma -1}$$ , $$t \ge 0$$ , $$1< \gamma < \frac{p^*_s}{p}$$ with $$p^*_s = \frac{Np}{N-sp}$$ , $$a- \frac{b}{\gamma }>0$$ with $$a,b\in \mathbb R_0^+: =[0, \infty )$$ , $$\lambda $$ is a parameter, $$q \in (1,p)$$ , $$(-\Delta )_{p}^s$$ is the fractional p-Laplace operator, $$V :\mathbb R^N\rightarrow \mathbb R^+: = (0, \infty )$$ is a potential function, h is a sign-changing weight function and f is a continuous function satisfying the Ambrosetti–Rabinowitz condition or not. To our best knowledge, the results here are the first contributions to the study of fractional Schrodinger–Kirchhoff type equations in which the Kirchhoff functions may be sign-changing and degenerate.