The concept of a pseudo almost periodic function on or , , generalizes the concept of an almost periodic (in sense of Bohr) function. A bounded on function is said to be pseudo almost periodic if , where is almost periodic on and satisfies the condition
The purpose of the paper is to establish existence of pseudo almost periodic solutions of linear and quasi-linear ordinary and parabolic partial differential equations. The following proposition is an emanation of the paper spirit:
Consider the system of the form , where is a complex matrix of is a vector function, whose components are pseudo almost periodic. If the matrix has no eigenvalues with real part zero, then this system admits a unique solution , whose components are pseudo almost periodic.