ABSTRACT
In Theorem 3.1, we show that if (1.2) has a unique ^-bounded solution, then it is periodic. Moreover, bounded solutions of (1.2) with initial functions converge to the periodic solution as / —> oo. Theorem 3.2 uses a growth and Lipschitz condition to obtain the uniqueness of periodic solutions of (1.2). Theorem 4.1 yields a periodic solution of a linear form of (1.2) using the theory of minimal solutions. For details on integral equations, see Burton [1], Corduneanu [3], and Gripenberg-Londen-Staffans [4]. For related results, see Burton-Furumochi [2] and Hino-Murakami [5].
