Abstract
Two results on the stability of a singular point of the differential equation
are proved, in the form of conditions on the functions f, g, h. The results are in the style of many results for Lienard's equation, and the proofs rest on the choice of a suitable Liapounov function. The arguments leading to this choice may be extended to any equation "close" to one for which a first integral may be obtained.
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References
W. Hahn (1967) "Stability of Motion", Springer, Berlin.
J.R.A. Pearson & C.J.S. Petrie (1970) "The flow of a tubular film. Part 2: Interpretation of the model and discussion of solutions.", J.Fluid Mech., 42, 609–625.
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© 1972 Springer-Verlag
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Petrie, C.J.S. (1972). A liapounov function for an automomous second-order ordinary differential equation. In: Everitt, W.N., Sleeman, B.D. (eds) Conference on the Theory of Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066950
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DOI: https://doi.org/10.1007/BFb0066950
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