EQUATIONS OF LYAPUNOV FOR OPERATORS WITH NLN-LOCAL BOUNDARY-VALUE CONDITIONS

Abstract

An operator equation of Lyapunov A (A=1, where A - operator, conjugate to A, 1 - single operator) is investigated in the paper aiming at the solution of an equation of Lyapunov for the case, when A and A - are non-self-conjugate differential operators of the second order with non-disintegrated regular boundary-value conditions. As a result the existence and uniqueness of the solution of an equation of Lyapunov for non-self-conjugate differential operators of the second order with regular non-disintegrated bounfary-value conditions have been proved. The explicit form of the solution has been found. The constructive approach to its search has been indicated. The paper results may find their field of application in the investigation of a spectrum of a non-self-conjugate differential operatorAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio