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oscillation problem; periodic differential equation; periodic solution; $\omega $-periodic solution; trigonometric polynomial; trigonometric approximation; Gram’s determinant
The present paper does not introduce a new approximation but it modifies a certain known method. This method for obtaining a periodic approximation of a periodic solution of a linear nonhomogeneous differential equation with periodic coefficients and periodic right-hand side is used in technical practice. However, the conditions ensuring the existence of a periodic solution may be violated and therefore the purpose of this paper is to modify the method in order that these conditions remain valid.
[1] N. K. Bobylev, J. K. Kim, S. K. Korovin et al.: Semidiscrete approximation of semilinear periodic problems in Banach spaces. Nonlinear Anal. 33 (1998), 473–482. DOI 10.1016/S0362-546X(97)00560-9 | MR 1635712
[2] B. M.  Budak, S. V. Fomin: Multiple Integrals and Series. Nauka, Moskva, 1971. (Russian) MR 0349912
[3] E. A. Coddington, N. Levinson: Theory of Ordinary Differential Equations. McGraw-Hill, New York-Toronto-London, 1955. MR 0069338
[4] P.  Hartman: Ordinary Differential Equations. John Wiley & Sons, New York-London-Sydney, 1964. MR 0171038 | Zbl 0125.32102
[5] V. N. Laptinskij: Fourier approximations of periodic solutions of nonlinear differential equations. Differ. Equ. 21 (1985), 1275–1280. MR 0818569 | Zbl 0617.34032
[6] L. A.  Liusternik, V. J. Sobolev: Elements of Functional Analysis. Nauka, Moskva, 1965. (Russian) MR 0209802
[7] I. G.  Main: Vibrations and Waves in Physics. Cambridge University Press, 1978, 1984, pp. 89–97.
[8] S. Timoshenko, D. H. Young: Advanced Dynamics. Mc Graw-Hill, New York-Toronto-London, 1948. MR 0028707
[9] L. Q.  Zhang: Spline collocation approximation to periodic solutions of ordinary differential equations. J. Comput. Math. 10 (1992), 147–154. MR 1159628 | Zbl 0776.65051
[10] L. Q.  Zhang: Two-sided approximation to periodic solutions of ordinary differential equations. Numer. Math. 66 (1993), 399–409. DOI 10.1007/BF01385704 | MR 1246964 | Zbl 0799.65077
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