Study On The Concentrated Solutions For A Class Of Schr?dinger Equations With Non-admissible Potential

We discuss the following nonlinear Schrodinger equation-?²?u+V(x)u=u^p-1,u>0,u?H¹(R^N),where ?>0 is a small parameter,N?2,2<p<2*.Here we mainly concern with local uniqueness and the number of concentrat-ed solutions of above nonlinear Schrodinger equation for a kind of non-admissible potential V(x)which possesses non-isolated critical points.First,we establish a more accurate location for the concentrated points,which will need an observation on the structure of the potential.Next,we prove local uniqueness for positive single-peak solutions.And then some results concerning on the number and symmetry of single-peak solutions are also given.In this paper,we generalizes M.Grossi's results in[12].