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 & where is a small positive parameter, a and b are positive constants, s (0, 1) and p (1, ∞) are such that, is the fractional p-Laplacian operator, f: → is a superlinear continuous function with subcritical growth and V: R3 → 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 + γur-1, where γ > 0 is sufficiently small, and the powers q and r satisfy 2p < q < ps≥ r. The main results are obtained by using some appropriate variational arguments