Almost Periodic Solutions for a Class of Functional Differential Equations

C. Corduneanu


The paper deals with functional differential equations of the form x'(t) = (Lx)(t) + (fx)(t), t E Rand x, f with values in then-dimensional Euclidean space. L is a linear continuous operator on the space of almost periodic functions with values in the n-dimensional Euclidean space, while f stands for a nonlinear operator on the same space. Assuming that the linear system x'(t) = (Lx)(t) has a unique almost periodic solution for each almost periodic right hand side, the paper provides condtions on f,under which the nonlinear system considered above enjoys a similar property. Both classical and functional analytic methods are necessary for obtaining the results. Examples are shown when the linear system possesses the property accepted as a basic hypothesis.

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