A class of KazdanWarner typed equations on noncompact Riemannian manifolds are discussed. Firstly

the existence and uniqueness of longtime solution to the corresponding heat equation with initial condition and Neumann boundary condition are obtained by the exhaustion method and the standard parabolic theory. And then

some uniform estimates of the solution to the heat equation are obtained and the existence and uniqueness of smooth solution to the equations discussed in this paper are gained under suitable conditions.