Existence and concentration of positive solutions for a critical p&q equation

We show existence and concentration results for a class of p&q critical problems given by -div (a (epsilon(p)vertical bar del u vertical bar(p)) epsilon(p)vertical bar del u vertical bar(p)(-2)del u) + V(z)b (vertical bar u vertical bar(p)) vertical bar u vertical bar(p-2) u = f(u) + vertical bar u vertical bar(q)*(-2) u in R-N, where u is an element of W-1,W-p(R-N) boolean AND W-1,W-q(R-N), epsilon > 0 is a small parameter, 1 < p <= q < N, N >= 2 and q* = Nq/(N-q). The potential V is positive and f is a superlinear function of C-1 class. We use Mountain Pass Theorem and the penalization arguments introduced by Del Pino & Felmer's associated to Lions' Concentration and Compactness Principle in order to overcome the lack of compactness.