Prescribing Chern scalar curvatures on noncompact manifolds

In this paper, we investigate the noncompact prescribed Chern scalar curvature problem which reduces to solve a Kazdan-Warner type equation on noncompact non-Kähler manifolds. By introducing an analytic condition on noncompact manifolds, we establish related existence results. As its another application, we further give a new proof of a classical multiplicity theorem of W.M. Ni.