MULTI-BUMP BOUND STATE SOLUTIONS FOR THE QUASILINEAR SCHRODINGER EQUATION WITH CRITICAL FREQUENCY

We study the existence of single- and multi-bump solutions of quasilinear Schrodinger equations -Delta u + lambda V (x) u - 1/2(Delta vertical bar u vertical bar(2))u = vertical bar u vertical bar(p-2)u, the function V being a critical frequency in the sense that inf(x is an element of RN) V(x) = 0. We show that if the zero set of V has several isolated connected components Omega(1),..., Omega(k) such that the interior of Omega(i) is not empty and partial derivative Omega(i) is smooth, then for lambda > 0 large, there exists, for any nonempty subset J subset of {1, 2, ...., k}, a standing wave solution trapped in a neighborhood of boolean OR Omega(j.)