On a Critical Exponential p & N Equation Type: Existence and Concentration of Changing Solutions

In this paper we study a class of quasilinear equation with exponential critical growth. More precisely, we show existence of a family of nodal solutions, i.e, sign-changing solutions for the problem {-div (a (epsilon(p)|del u|(p)) epsilon(p)|del u|(p-2) del u) + V( z)b (|u|(p) |u|(p-2)u = f (u) in R-N, u is an element of W-1,W- p(R-N) boolean AND W-1,W-N (R-N). Such nodal solutions concentrate on the minimum points set of the potential V, changes sign exactly once in R-N and have exponential decay at infinity. Herewe use variational methods and Del Pino and Felmer's technique (Del Pino and Felmer 1996) in order to overcome the lack of compactness.