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- W2060600121 abstract "1. This paper is concerned with certain asymptotic properties of the solutions of the differential equation where dots indicate differentiation with respect to t, k is a small parameter, and f ( x, ẋ, t ) satisfies certain conditions which will be formulated below. Equations of this type occur frequently in non-linear mechanics; for k = 0 a system satisfying (1·1) behaves as a harmonic oscillator. To ensure the existence and uniqueness of the solutions of (1·1) it must be assumed that the right-hand side is bounded and satisfies a Lipschitz condition, at least for finite x, ẋ and say all t ≥ 0. The parameter k may be considered as a measure of the ‘smallness’ of the upper bound, and of the Lipschitz constant, of the right-hand side, and need not have any intrinsic physical significance." @default.
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- W2060600121 date "1950-07-01" @default.
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- W2060600121 title "On the asymptotic behaviour of the solutions of a class of non-linear differential equations" @default.
- W2060600121 doi "https://doi.org/10.1017/s0305004100025925" @default.
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