Interrelated Almost Periodicity Of The Solutions Of DIRICHLET Problem

Since Danish mathematician H. Bohr established almost periodic functions theory from 1925 to 1926, the main feature of almost periodic functions theory's development in basic properties of functions has been extended in its scope. From almost periodic functions, uniform almost periodic functions, asymptotically almost periodic functions, weakly almost periodic functions to pseudo almost periodic functions which were proposed by Professor Zhang Chuanyi in 1992, the applications of almost periodic functions and the solutions of differential equations have been improved in each time. Almost periodic functions which have important applications in partial differential equation, have been developed a lot through hard work of several generations of mathematicians, but many problems remain to be solved.The paper has two parts: one part extended the conclusion of almost periodic properties of the solutions of two dimensional equations to that of n dimensional equations, the other part is on the discussion of almost periodic properties of the solutions of Dirichlet problem for Poisson equations on half space. Specific as follows:Firstly, based on the known result of almost periodic properties of the solutions of two dimensional harmonic equation, by using the basic theory of almost periodic functions, the paper discussed the correlative almost periodic properties when the data of Dirichlet problem of harmonic equation on n dimensional half space.Secondly, similar to the discussion of harmonic equation, the correlative almost periodic properties of the solutions of Dirichlet problem for two dimensional and n dimensional Poisson equations are discussed.