Existence and concentration of solutions for a quasilinear elliptic field equation

In this paper, we study the existence and concentration of solution for the following class of quasilinear problem -(h) over bar (2) Delta v + V(x)v - (h) over bar (p) Delta(p)v + W' (v) = 0 x is an element of R-N, (P-(h) over bar) when (h) over bar 0 is small enough, where v : R-N -> RN+1, 3 <= N < p, <(h)over bar> > 0, W is a C-1 singular functional that satisfies some technical conditions and the potential V is continuous functions with lim inf(vertical bar x vertical bar ->+infinity) V(x) equivalent to V-infinity > inf(x is an element of RN) V(x) > 0. Moreover, we also consider the existence of solution for all (h) over bar > 0 when V is a radial function.