Existence of Multi-bump Solutions for a Class of Quasilinear Schrodinger Equations in Involving Critical Growth

In this paper we prove the existence of multi-bump solutions for a class of quasilinear Schrodinger equations of the form in the whole space, where h is a continuous function, are continuous functions. We assume that V(x) is nonnegative and has a potential well consisting of k components such that the interior of Omega (i) is not empty and is smooth. By using a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem for suitable assumptions. We show that for any given non-empty subset. , a bump solution is trapped in a neighborhood of for large enough.