We consider the Dirichlet problem for poly harmonic operators and Navier problem in a half space.First,under some very mild growth conditions,we show that the Dirichlet problem is equivalent to the integral equation.And we also prove the equivalence between Navier problem and integral equation without any assumption on.Secondly,we obtain Liouville theorems for these two problems.Finally,we present the applications for both Liouville theorems.