Accession Number : AD0681782

Title :   CONSTRUCTION OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH QUASI-PERIODIC COEFFICIENTS,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Mitropolskii,Yu. A. ; Samoilenko,A. M.

Report Date : 03 SEP 1968

Pagination or Media Count : 20

Abstract : The authors consider the problem of constructing a general solution of the system dx/dt = Ax + P(omega t)x, the right-hand side of which is smooth and quasi-periodic with respect to t with a frequency basis omega = (omega sub 1,...,omega sub n). When specific conditions are imposed on A, omega and P(omega t) it is proved that the solution of the above system has the form x = phi(omega t)e to the power ((A sub o)t) x sub o, where phi(omega t) is a quasi-periodic matrix with the same frequency basis omega = (omega sub 1,...,omega sub n) and a rapidly converging process for the construction of the matrices phi (omega t) and A sub o is given.

Descriptors :   (*DIFFERENTIAL EQUATIONS, PERIODIC VARIATIONS), APPROXIMATION(MATHEMATICS), FOURIER ANALYSIS, MATRICES(MATHEMATICS), CONVERGENCE, SERIES(MATHEMATICS), USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE