Dirichlet problem for anisotropic prescribed mean curvature equation on unbounded domains

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In this paper, we consider the Dirichlet problem for hypersurfaces M=graphu of anisotropic prescribed mean curvature H=H(x,u,N) on unbounded domain Ω, where N is the unit normal to M at (x,u). As a corollary of the result, we obtain the existence of translating solutions to the mean curvature flow with a forcing term on unbounded domains. The approach used here is a modified version of classical Perron's method, where the solutions to minimal surface equation are used as supersolutions and a family of auxiliary functions is constructed as local subsolutions.