Semiclassical states for a class of nonlinear elliptic field equations

In this paper we are concerned with the problem of finding solutions for the following nonlinear field equation -(h) over bar (2)Deltav+V(x)v-(h) over bar (p)Delta(p)v+W'(v)=0, where v : R-N-->RN+1, Ngreater than or equal to3, p>N, (h) over bar >0, the potential V is positive and W is an appropriate singular function. Assuming that V has a mountain pass geometry, determined by the existence of two strict local minima, then for small values of the parameter (h) over bar we are able to find a solution which concentrates at the related mountain pass point of V in the semiclassical limit (i.e., as (h) over bar -->0(+)). The proof of our results uses a variational approach and the solutions are captured as critical points for the associated energy functional.