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- W2087165462 abstract "x’ =f(t, x), x&J = x0 , (0.1) with f continuous, is well posed in the sense that it has the property of existence uniqueness and continuous dependence of solutions upon the data. Moreover, when a solution exists, it is very useful to approach it by means of some constructive method, for instance using the classical Peano-Picard method of the successive approximations. It is a well known fact that the continuity of the vector fieldf is not sufficient to ensure uniqueness or convergence of successive approximations and, in infinite dimension, even existence of solutions [16, 61. These pathologies are however ruled out if f is supposed to satisfy some additional hypotheses, for instance if f is locally Lipschitzian. It is then quite natural to raise the problem whether the set of all “nice” continuous f for which problem (0.1) is well posed and/or the corresponding successive approximations converge to a solution of (0.1) is larger, in a sense to be specified, than its complement. To make the question meaningful we say that a property is generic in a Baire space if the subset on which it is not true is meager or, equivalently, if the property is true on a residual subset. Here by meager set we mean a set of Baire first category. Thus a generic property is one which is possessed by almost all" @default.
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- W2087165462 date "1979-02-01" @default.
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- W2087165462 title "Some generic properties of functional differential equations in Banach spaces" @default.
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- W2087165462 doi "https://doi.org/10.1016/0022-247x(79)90035-0" @default.
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