Positive Solutions For Generalized Quasilinear Schrodinger Equations With Asymptotically Linear Nonlinearities

In this paper, we study the following generalized quasilinear Schrodinger equations-div(g(2))(u)del u) + g(u)g' (u)vertical bar del u vertical bar(2) + V(x)u = h(u) = h(u), x is an element of R-N,where N >= 3, V is an element of C(R-N, R+) is a given potential, g is a C-1 even function with g'(t) <= 0 for all t >= 0, g(0) = 1, lim(t ->+infinity) g(t) = a, 0 < a < 1. The nonlinearity h is an element of C-1(R, R) satisfies asymptotically linear at infinity. Under certain assumptions on V, g and h, we give the existence results via variational methods. Moreover, we give an application for our results.