New Solutions for nonlinear Schrödinger equations with critical nonlinearity

We consider the following nonlinear Schrödinger equations in ℝⁿ [**EQUATION**] where V (r) is a radially symmetric positive function. In [2] Ambrosetti, Malchiodi and Ni proved that if [**EQUATION**] has a nondegenerate critical point r₀ ≠ 0 then a layered solution concentrating near r₀ exists. In this paper, we show that if [**EQUATION**] and the dimension n= 3, 4 or 5, another new type of solution exists: this solution has a layer near r₀ and a bubble at the origin.