On existence and concentration of positive bound states of p-Laplacian equations in RN involving critical growth

This paper deals with the study of the quasilinear critical problem(Pε)-εpΔpu+V(z)up-1=f(u)+up*-1inRN,u∈Cloc1,α(RN)∩W1,p(RN),u>0inRN,where ε is a small positive parameter; f is a subcritical nonlinearity; p*=pN/(N-p), 1infΩV for some open bounded subset Ω of RN. We study whether we can find solutions of (Pε) which concentrate around a local minima of V, not necessarily nondegenerate. The proof of this result is variational based on the local mountain-pass theorem.