SOLVABILITY OF FUNCTIONAL-DIFFERENTIAL EQUATIONS OF n-ORDER IN HILBERT SPACE

Solvability problems for functional-differential equations (FDE) of n-order with unbounded operator coefficients in Hilbert space are investigated in the paper aiming at the obtaining of necessary and sufficient conditions of the unambiguous solvability for an equation with constant operator coefficients and argument deviations on the whole axis. The conditions clarification of the unambiguous solvability of a "small" disturbed equation is also the aim of the paper as well as the problem clarification of the normal solvability in the general case. The results obtained complete the theory of abstract FDE of highest orders and may be used in the fields, in which equations of highest orders origitane. Conditions on a resolvent, argument deviations and coefficients of an equation of n-order, conditions ensuring the unambiguous and normal solvability of an equation, have been obtained. Theorems of necessary and sufficient conditions of the unambiguous solvability of an equation with coefficients and argument deviations have been proved as well as some theorems of the unambiguous solvability in the general case and the theorem of the normal solvabilityAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio