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The Poincaré-Bendixson theorem for certain differential equations of higher order. (English) Zbl 0408.34042


MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
35G30 Boundary value problems for nonlinear higher-order PDEs
35B10 Periodic solutions to PDEs
37D99 Dynamical systems with hyperbolic behavior
70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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References:

[1] DOI: 10.1216/RMJ-1977-7-3-457 · Zbl 0373.34021
[2] Hirsch, Differential Equations, Dynamical Systems, and Linear Algebra (1974)
[3] Burkin, Sibirsk. Mat. Z. 18 pp 251– (1977)
[4] Borg, K. Tekn. Högsk. Handl. 153 pp 12– (1960)
[5] Vaisbord, Mat. Sb. 56 pp 43– (1962)
[6] Smith, Proc. Roy. Soc. Edinburgh Sect. A 79 pp 327– (1977) · Zbl 0417.34073
[7] Smith, Proc. Roy. Soc. Edinburgh Sect. A 76 pp 31– (1976) · Zbl 0348.34032
[8] DOI: 10.1112/jlms/s2-7.2.203 · Zbl 0269.34043
[9] DOI: 10.2307/2373135 · Zbl 0116.06803
[10] Pliss, Nonlocal Problems of the Theory of Oscillations (1966)
[11] DOI: 10.1002/zamm.19690490307 · Zbl 0175.10302
[12] DOI: 10.1080/00207177108931977 · Zbl 0219.93014
[13] Newman, Elements of the Topology of Plane Sets of Points (1951) · Zbl 0045.44003
[14] Mirsky, An Introduction to Linear Algebra (1955) · Zbl 0066.26305
[15] DOI: 10.1007/BF00975894 · Zbl 0295.34029
[16] DOI: 10.1016/0022-247X(61)90059-2 · Zbl 0105.29301
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.