The admissibility of periodic processes and existence theorems for periodic solutions. II (Q1390456)

The authors consider systems of the form \[ x' = A(t,x)x +B(t,x) f(t,x), \tag{1} \] where \( A: \mathbb{R}^{1+n} \to \Hom(\mathbb{R}^n, \mathbb{R}^n), B: \mathbb{R}^{1+n} \to \Hom( \mathbb{R}^{n}, \mathbb{R}^{n}),\) \( f: \mathbb{R}^{1+n} \to \mathbb{R}^{m} \) are functions with specific properties. Further let \( X: \mathbb{R} \to \Omega (\mathbb{R}^n) \) be a given function. The paper contains theorems which give sufficient conditions for the existence of at least one \(T\)-periodic solution to (1), with \( x(t) \in X(t)\). For part I see [Russ. Math. 40, No. 11, 65-72 (1996); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1996, No. 44(414), 62-69 (1996; Zbl 0907.34027)].