Quasilinear Schrodinger equations with superlinear terms describing the Heisenberg ferromagnetic spin chain

In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain: -Delta u + V(x)u - u/root 1 - u(2) Delta root 1 - u(2) = c vertical bar u vertical bar(p-2)u, x is an element of R-N, where 2 < p < 2*, c > 0 and N >= 3. By the cutoff technique, the change of variables and the L-infinity estimate, we prove that there exists c(0) > 0, such that for any c > c(0) this problem admits a positive solution. Here, in contrast to the Morse iteration method, we construct the L-infinity estimate of the solution. In particular, we give the specific expression of c(0).