Abstract
Assume that the right-hand side f of the differential equation (0.1) does depend on certain derivatives Du of the function u looked for, i. e., a partial differential equation of type (0.3) is to be investigated instead of an ordinary differential equation (0.1). Differential operators D entering into the right-hand side f of (0.3) are not bounded, in general. That is why in a fixed Banach space the initial value problem (0.3), (0.2) cannot be solved by using the method of successive approximations regarded in section 1.5.
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© 1989 Springer-Verlag Berlin Heidelberg
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Tutschke, W. (1989). Scales of Banach Spaces. In: Solution of Initial Value Problems in Classes of Generalized Analytic Functions. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09943-8_3
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DOI: https://doi.org/10.1007/978-3-662-09943-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50216-6
Online ISBN: 978-3-662-09943-8
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