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G. M.
Partial Differential EquationsNature, 75
Di erential Equations, Vol. 37, No. 6, 2001, pp. 763{767. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 6, 2001, pp. 730{734. Original Russian Text Copyright c 2001 by Demenchuk. ORDINARY DIFFERENTIAL EQUATIONS Quasiperiodic Solutions of Linear Nonhomogeneous Di erential Equations A. K. Demenchuk Institute for Mathematics, National Academy of Sciences, Belarus Received February 2, 2000 Consider the system x _ = A(t)x + '(t);x 2 R ; (1) where A(t) is a quasiperiodic n n matrix function with frequency basis and '(t) is a quasiperi- odic n-vector function with frequency basis . For linear systems, quasiperiodic solutions whose frequency basis coincides with that of the right-hand side were quite comprehensively investigated (e.g., see [1, 2] and other papers). Samoilenko [3] constructed a theory for analyzing quasiperiodic solutions of di erential equations with the use of Green functions. This approach was applied in [4] to system (1) with a constant matrix A and with nonhomogeneity in the form of a trigonometric polynomial. However, system (1) can have other relations between the frequency bases of solutions and the right-hand side. For example, the form and existence conditions for solutions with irrational ratio of the period to that of the
Differential Equations – Springer Journals
Published: Oct 12, 2004
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