The Existence Of Infinitely Many Solutions For The Prescribed Boundary Mean Curvature Problem In B~N

The prescribed boundary mean curvature problem is a kind of important problems in confor-mal geometry.The paper studies the prescribed boundary mean curvature problem in BN,which is equivalent to the following equationwhereas K(x)is a bounded continuous function in RN-1,with a sequence of strictly local maximum points zj such that ?zj??+?,and has the following expansion near each zjBy using finite dimension reduction method,we only need to find critical points of functional in finite dimension domain,rather than find critical points of the energy functional I(u)of the above equation.Therefore we know infinitely many positive solutions of the equation,meanwhile,these solutions has two local maximum points,and the distance of them is very large.