Soliton solutions for quasilinear modified Schrödinger 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 1 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).