We study the existence and concentration of positive solutions for the following class of fractional ▫$p$▫-Kirchhoff type problems: ▫$$ \begin{cases} \left(\varepsilon^{sp}a+\varepsilon^{2sp-3}b ...\,[u]_{s, p}^{p}\right)(-\Delta)_{p}^{s}u+V(x)u^{p-1}=f(u) & \text{in}\; \mathbb{R}^{3},\\ u\in W^{s, p}(\mathbb{R}^{3}), \quad u>0 & \text{in}\; \mathbb{R}^{3}, \end{cases}$$▫ where ▫$\varepsilon$▫ is a small positive parameter, ▫$a$▫ and ▫$b$▫ are positive constants, ▫$s \in (0, 1)$▫ and ▫$p \in (1, \infty)$▫ are such that ▫$sp \in (\frac{3}{2}, 3)$▫, ▫$(-\Delta )^{s}_{p}$▫ is the fractional ▫$p$▫-Laplacian operator, ▫$f \colon \mathbb{R} \to \mathbb{R}$▫ is a superlinear continuous function with subcritical growth and ▫$V \colon \mathbb{R}^3 \to \mathbb{R}$▫ is a continuous potential having a local minimum. We also prove a multiplicity result and relate the number of positive solutions with the topology of the set where the potential ▫$V$▫ attains its minimum values. Finally, we obtain an existence result when ▫$f(u) = u^{q-1} + yu^{r-1}$▫, where ▫$y> 0$▫ is sufficiently small, and the powers ▫$q$▫ and ▫$r$▫ satisfy ▫$2p < q < p^*_s \le r$▫. The main results are obtained by using some appropriate variational arguments.
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