Existence of Multiple Solutions for Fractional p-Kirchhoff Equation with Critical Sobolev Exponent

In this paper, using the concentration-compactness principle and a version of the symmetry mountain pass theorem, we show the existence and multiplicity of solutions to the following fractional p-Kirchhoff equations with critical nonlinearity: [GRAPHICS] . where a, b > 0 are constants, (-Delta)(p)(s) is the fractional p-Laplacian operator with 0 < s < 1 < p < infinity, Omega is a bounded domain in R-N with smooth boundary, 2sp > N > sp, mu is a positive parameter and f : Omega x R -> R is a Caratheodory function.