Soliton solutions for quasilinear modified schrodinger equations in applied sciences

In this paper, we prove the existence of nontrivial weak bounded solutions of the quasilinear modified Schrodinger problem {-div(g(2))(u)del u) + g(u)g'(u)vertical bar del u vertical bar(2) + V(x)u = f(x,u) in R-3, u > 0 in R-3, where V -+ R-3 -> R, f: R(3)x R -> R are "good" functions and g : R -> R is such that g(2) (u) = 1 + [(l(u(2)))'](2)/2 for a given l is an element of C-2 (R). By means of variational methods and an approximation argument, here we obtain an existence result for the superfluid film equation in Plasma Physics and for the equation which models the self-channelling of a high-power ultrashort laser, which derive from our model problem by taking l(s) = s, respectively l(s) = root 1+s, in the previous definition of g(2) (u).