Necessary and sufficient conditions for the existence and uniqueness of a bounded solution of the equation dx(t)/dt = f(x(t) + h1(t)) + h2(t)

Necessary and sufficient conditions for a bounded solution of the nonlinear scalar differential equation dx(t)/dt = f(x(t) + h(1)(t)) + h(2)(t), t is an element of R, to exist and be unique are presented in the case when f(x) is a continuous function and the functions h(1)(t) and h(2)(t) are bounded and continuous. The case when h(1)(t) and h(2)(t) are almost periodic functions is also investigated. Bibliography: 31 titles.