Existence and Concentration Result for a Fractional p‐Kirchhoff Type Equation With Critical Growth

ABSTRACT

In this paper, we study the following fractional ‐Kirchhoff equation with critical growth: where is a small parameter, denotes the fractional ‐Laplacian operator with , and is the fractional critical Sobolev exponent. is the Kirchhoff function, is a continuous function with subcritical growth and is a positive continuous potential. Using the penalization method and Ljusternik‐Schnirelmann theory, we show that the existence, multiplicity, and concentration of nontrivial solutions as sufficiently small.