Existence and Asymptotic Behavior of Positive Solutions for a Class of Quasilinear Schrödinger Equations

In this paper, we study the quasilinear Schrödinger equation , , where is a given potential, , and either , for or for . If for some , we establish the existence of a positive solution satisfying as for any . Particularly, if , we prove the existence of a positive classical radial solution and up to a subsequence, in as , where is the ground state of the problem ,