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- W137365094 abstract "£y + f(x,y,y',6) = O, 0 0 is a small parameter and prime denotes differentiation with respect to x. We shall formulate conditions under which the problem (i.i), (1.2) has a unique solution y(x, e) existing on the entire interval [0,b], for e sufficiently small. We shall also obtain explicit bounds on y(x,E) and y' (x,e) as g + 0. In particular, we find conditions under which y(x,£) is uniformly bounded as g + 0. The conditions we place on f(x,y,z,£) are quite different from the standard uniform Lipschitz condi~f tion; other than smoothness, our essential requirements are that f3(x,y,z,e) ~)z ~f be strictly positive and bounded away from zero and that f2(x,y,z,£) ~ be bounded above o_nl_~ for z = 0. The precise conditions are stated below. We shall indicate a couple of applications of our results at the end. More serious applications will hopefully appear elsewhere. The spirit of this work is very close to that of [i] and [2]." @default.
- W137365094 created "2016-06-24" @default.
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- W137365094 date "1974-01-01" @default.
- W137365094 modified "2023-09-27" @default.
- W137365094 title "Singularly perturbed initial value problems" @default.
- W137365094 cites W1986211347 @default.
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- W137365094 doi "https://doi.org/10.1007/bfb0065507" @default.
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