On a Class of Nonlinear Schrödinger Equations in 2 Involving Critical Growth

In this paper we deal with semilinear elliptic problem of the form where is a small positive parameter, V: 2→ is a positive potential bounded away from zero, and f(u) behaves like exp(αs2) when s→+∞. We prove the existence of solutions concentrating around a local minima not necessarily nondegenerate of V(x), when tends to 0.