A family of solutions of certain nonautonomous differential equations by series of exponential functions
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_ R2 _ Rp base of frequencies Cauchy's inequality change of coordinates CLEMSON UNIVERSITY coefficient and finite complex number components composite transformation consider the differential converges defined and analytic defined by 2.5 differential equation 3-3 equation with odd EQUATIONS BY SERIES exists an invertible EXPONENTIAL FUNCTIONS family of periodic FAMILY OF SOLUTIONS finite Fourier series Fourier-Taylor FUNCTIONS By T. G. Gelmand H. H. Suber iff Nm inequality 1.2 J=l J J l-nb Lemma mp=n p prime n-vector n+v+2 Nn e I2k Nn«ft Nn*fi NneI2k NONAUTONOMOUS DIFFERENTIAL EQUATIONS odd periodic coefficient period 2tt periodic solutions polydisk positive number Prepared under Grant Proctor and H. H. proof quasi-periodic recursion Ricatti equation right side satisfy SERIES OF EXPONENTIAL solution of 4.1 solution of equation solution with mean sufficiently small T. G. Proctor Theorem 2.1 uniformly and absolutely vector differential equation write yn y y b y y„y c