Concentration of positive solutions for a class of fractional p -Kirchhoff type equations

We study the existence and concentration of positive solutions for the following class of fractional p-Kirchhoff type problems: 0 & ext{in} mathbb{R}^{3}, end{array} ight.$$]]> where E is a small positive parameter, a and b are positive constants, s â (0, 1) and p â (1, ∞) are such that, is the fractional p-Laplacian operator, f: â., → â., is a superlinear continuous function with subcritical growth and V: â.,3 → â., 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) = uq-1 + Î3ur-1, where γ> 0 is sufficiently small, and the powers q and r satisfy 2p < q < p∗s â