Right-Sided Invertibility of Binomial Functional Operators and Graded Dichotomy

In this paper, we consider the right-sided invertibility problem for binomial functional operators. It is known that such operators are invertible iff there exists dichotomy of solutions of the homogeneous equation. A new property of solutions of the homogeneous equation named graded dichotomy is introduced and it is proved that the right-sided invertibility of binomial functional operators is equivalent to the existence of graded dichotomy.