The existence of semiclassical states for some <Emphasis Type="Italic">p</Emphasis>-Laplacian equation with critical exponent

In this paper, we study the existence of semiclassical states for some p-Laplacian equation. Under given conditions and minimax methods, we show that this problem has at least one positive solution provided that ε ≤ E; for any m ∈ ?, it has m pairs solutions if ε ≤ E _m , where E, E_m are sufficiently small positive numbers. Moreover, these solutions are closed to zero in W^1,p(? ^N ) as ε → 0.