Application of the Bubnov-Galerkin procedure to the problem of searching for selfoscillations. (English. Russian original) Zbl 0299.34053
J. Appl. Math. Mech. 37, 963-967 (1973); translation from Prikl. Mat. Mekh. 37, 1015-1019 (1973).
MSC:
| 34C25 | Periodic solutions to ordinary differential equations |
| 42A10 | Trigonometric approximation |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34A45 | Theoretical approximation of solutions to ordinary differential equations |
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
References:
| [1] | Stokes, A., On approximations of nonlinear oscillations, (Proc. Fifth International Conf. on Nonlinear Oscillations (1969), Vol. 2 (1970)), Kiev · Zbl 0234.34050 |
| [2] | Urabe, M., Galerkin’s procedure for nonlinear periodic systems, Arch. Rational Mech. Anal., Vol. 20, N≗2 (1965) · Zbl 0133.35502 |
| [3] | Bobylev, N. A.; Krasnosel’skii, M. A., Parameter functionalization and a contiguity theorem for autonomous systems, Differentsial’nye Uravneniia, Vol. 6, N≗11 (1970) · Zbl 0265.34009 |
| [4] | Zabreiko, P. P.; Strygina, S. O., On periodic solutions of evolution equations, Matem. Zametki, Vol. 9, N≗6 (1971) · Zbl 0228.34039 |
| [5] | Strygin, V. V., Contiguity theorems for the periodic problem of an autonomous system of ordinary differential equations, (Seventh Summer Math. School (1969). Seventh Summer Math. School (1969), Kiev. (1970)) · Zbl 0272.34083 |
| [6] | Shimanov, S. N., On the theory of vibrations of quasi-linear systems with lag, PMM, Vol. 23, N≗ 5 (1959) · Zbl 0101.06803 |
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