On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations

Abstract

This paper is concerned with the existence of almost periodic solutions of neutral functional differential equations of the form d dt Dxt = Lxt + f (t), where D, L are bounded linear operators from Cf is an almost (quasi) periodic function. We prove that if the set of imaginary solutions of the characteristic equations is bounded and the equation has a bounded, uniformly continuous solution, then it has an almost (quasi) periodic solution with the same set of Fourier exponents as f .

Affine‐periodic orbits for linear dynamical systems

“…2 But this does not hold for linear almost periodic systems in the absence of Favard's separability. [3][4][5] For some new developments, one can see previous studies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and references therein. In the last decades, a great deal of attention has been paid to study the spatio-temporal patterns, e.g., rotating spiral waves.…”