Functional Differential Equations by Corduneanu Constantin; Li Yizeng; Mahdavi Mehran & YIZENG LI & MEHRAN MAHDAVI

Author:Corduneanu, Constantin; Li, Yizeng; Mahdavi, Mehran & YIZENG LI & MEHRAN MAHDAVI
Language: eng
Format: epub, mobi
Publisher: Wiley
Published: 2016-05-09T00:00:00+00:00

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OSCILLATORY MOTION, WITH SPECIAL REGARD TO THE ALMOST PERIODIC CASE

The oscillatory solutions (e.g., periodic and almost periodic) constitute a wide preoccupation of researchers, and several monographs have been dedicated to the subject. Recently, relatively new classes of almost periodic solutions have made their way into the literature (see Shubin [496,497], Corduneanu [161], a.o.). For most of these classes, the series approach can be applied, even in nonlinear cases.

In this chapter, we define the APr-almost periodic functions and establish basic properties (the case of the function defined on R). Of course, we have in mind applications to various classes of functional equations, namely ordinary differential equations, integral equations, and convolution equations. The convolution extends from the classical cases, to functions in APr-almost periodic spaces. This chapter also provides several examples of functional differential or integro-differential equations, with regard to the existence of APr-almost periodic solutions, solutions in Besicovitch spaces of almost periodic functions, and also in the classical case (Bohr).

We would like to note that the role of series is considerably increased, in comparison to the frequency in the mathematical literature nowadays. That is why one of the most significant aspects in connection with their applications to functional equations is the problem (to be solved!) of reconstructing the function when we know its series. This problem is much simpler in classical approaches.

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