Construction Of Solutions For Neumann Problem With A Critical Nonlinearity On Boundary Via Local Pohozaev Identities

In this paper,we study the following Neumann problem with a critical nonlin-earity on boundary whereD1,2 denotes the completion of Co?(R+N)under the norm ?R+N|?u|2,y=(y',y)?R2×RN-3,K(y)=K(|y'|,y)is a bounded nonnegative function,2#=2(N-1)/(N-2)is the critical exponent of the Sobolev trace embedding.In this paper,introducing some local Pohozaev identities into the finite-dimensional reduction method,we prove that if N?5 and K(r,y)has a stable critical point(r0,y0),r0>0,such that K(r0)>0,then the above problem has infinitely many solutions.Our results generalize the results in[22],which includes the case that the critical points of K(r,y)are saddle points.