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UBC Theses and Dissertations

Existence of periodic solutions of certain non-linear differential equations Butkov, Eugene


The theory of Poincaré and Bendixson is applied to establish the existence of periodic solutions of the differential equation ẍ + f(x, ẋ)ẋ + g(x) x = 0 One part of the work is concerned with those equations which can be considered as arising from small perturbations of other equations of the same type, already possessing periodic solutions. Two existence theorems are demonstrated and the stability and uniqueness of the periodic solutions is also discussed. The other part contains several, theorems stating sufficient conditions for existence of periodic solutions which cannot be treated by perturbation methods.

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