Multiplicity and concentration of solutions for elliptic systems with vanishing potentials

In this article we use variational methods to study a strongly coupled elliptic system depending on a positive parameter lambda. We suppose that the potentials are nonnegative and the intersection of the sets where they vanish has positive measure. A technical condition, imposed on the product of the potentials, allows us to consider a setting where we do not assume any positive lower bound for the potentials. Considering the associated functional, defined on an appropriated subspace of D(1,2)(R(N)) x D(1,2)(R(N)), we are able to establish results on the existence and multiplicity of solutions for the system when the parameter lambda is sufficiently large. We also study the asymptotic behavior of these solutions when lambda -> infinity. (C) 2010 Elsevier Inc. All rights reserved.