Affine-periodic solutions for nonlinear differential equations

Abstract

The existence of affine-periodic solutions is studied. These types of solutions may be periodic, harmonic or even quasi-periodic. Mainly, via the topological degree theory, a general existence theorem is proved, which asserts the existence of affine-periodic solutions, extending some classical results. The theorem is applied to establish the Lyapunov function type theorem and the invariant region principle relative to affine-periodic solutions.