Existence, multiplicity and concentration of bound states for a quasilinear elliptic field equation

In this paper we study existence, multiplicity and concentration of solutions for the following nonlinear field equation where the potential V is positive and W is an appropriate singular function. Here is regarded as a small parameter. Under suitable conditions on V and W we find solutions exhibiting a concentration behaviour at an absolute minimum of V as Such solutions are obtained as local minima for the associated functional; the proofs of our results rely on a careful analysis of the behaviour of minimizing sequences and use arguments inspired by the concentration-compactness principle. Received July 21, 1999; Accepted April 9, 2000 / Published online September 14, 2000