The Existence Of Nontrivial Solutions For P-Kirchhoff Type Equations With Critical Exponent In R~N

We study the existence of nontrivial solutions of the p-Kirchhoff type equationwith critical nonlinearity, where a?0, b>0, 1<p< N,1 < q < p,p* =Np/N-p,??0,?pu = div(|?u|p-2?u) is the p-Laplacian of u, f?Lp*/p*-q(RN) \ {0} and is nonnegative.Under certain conditions, we proved the existence of at least two nontrivial solutions of equation (0.1) by the methods of Ekeland variational principle and the mountain pass the-orem. The main work of this paper is to generalize the results of Kirchhoff type equation in [22] to p-Kirchhoff type equation.