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

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.

Document Details

Document Type
Technical Report
Publication Date
Sep 03, 1968
Accession Number
AD0681782

Entities

People

  • A. M. Samoilenko
  • Yu. A. Mitropolskii

Organizations

  • Johns Hopkins University Applied Physics Laboratory

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Coefficients
  • Construction
  • Differential Equations
  • Equations
  • Frequency
  • Linear Differential Equations
  • Mathematical Analysis
  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Linear Algebra