Existence Of Multi-peak Solutions Of Kirchhoff Equation

In this paperm we study the following Kirchhoff problem(?)x?Rn,n?1,x?Rn,n?1,where a,b>0,0<??1,1<p<2*-1,2*is the critical Sobolev embedding index and ?>0 is a parameter,V(x)satisfies some assumptions.First,we discuss the existence and non-degeneracy of the solutions to the "limit equations" for the above problem.Second,when ?>0 is sufficient small,we obtain multi-peak solutions u?of the above problem by using lyapunov-schmidt reduction method and we prove that the solutions {u?} concentrate at a minimal point of V(x).