Foliations by stationary disks of almost complex domains

We study the problem of existence of stationary disks for domains in almost complex manifolds. As a consequence of our results, we prove that any almost complex domains which is a small deformations of a strictly linearly convex domain $D \subset C^n$ with standard complex structure admits a singular foliation by stationary disks passing through any given internal point. Similar results are given for foliation by stationary disks through a given boundary point