The Existence And Asymptotic Behavior For The Solution Of Fractional P-Kirchhoff Equation

In the paper,we consider the existence and asymptotic behavior of the solution of fractional p-kirchhoff equationwhere 0<s<1<p<?,N>ps,?,??R~N,?p<q<p_s~?,??[1,N/(N-ps)),p_s~?=Np/(N-ps) is the critical exponent in the sense of Sobolev.In chapter one,the background and current research for problem that we deal with are presented.Then the paper's framework and main results are also summa-rized.In chapter two,some essential preparatory results are stated.In chapter three,based on the method and idea of some existing results for frac-tional p-kirchhoff equation,the existence and asymptotic behavior in non-degenerate situation are studied by using Mountain Pass Lemma.In chapter four,the existence and asymptotic behavior of the solution for de-generate fractional p-kirchhoff equation are considered.