INVERTIBILITY OF NONAUTONOMOUS FUNCTIONAL-DIFFERENTIAL OPERATORS
V. Yu. Slyusarchuk · Mathematics of the USSR-Sbornik · 1987
Let be the Banach space of continuous and bounded functions on that take values in a finite-dimensional Banach space and have derivatives up to and including order . The norm in is given by is the Banach space of -periodic functions with the same norm as .Theorem. Suppose 1) is a -completely continuous element of the space (); 2) ; 3) there exists a completely continuous operator () for which and Then the operator has a -continuous inverse.Using this theorem the invertibility of a large class of operators is studied, which class contains in particular Poisson stable operators.Bibliography: 22 titles.