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## Kneser's theorem for weak solutions of an mth-order ordinary differential equation in Banach spaces

### Authors:

- Stanisław Szufla

### Abstract

The Kneser's theorem of an mth-order ordinary differential equations in Banach spaces is presented. It is assumed that I = [0,a] is a compact interval in R, E is a sequentially weakly complete Banach space, B = {x∈E:∥x∥≤b} and f:I×B→E is a weakly-weakly continuous function such that ∥f(t,x)∥≤M for (t,x)∈I×B. The Cauchy problem x^{(m)} = f(t,x), x(0) = 0,x′(0) = η_{1}, ..., x^{(m-1})(0) = η_{m-1}, where m≥1 and η_{1}, ..., η_{m-1}∈E and x^{(m)} means the mth-order derivative in the weak sense is considered.

- Record ID
- UAMbd9fdc1ab54944468b8f269773cfe8e9
- Author
- Journal series
- Nonlinear Analysis-Theory Methods & Applications, ISSN 0362-546X
- Issue year
- 1999
- Vol
- 38
- Pages
- 785-791
- ASJC Classification
- ;
- DOI
- DOI:10.1016/S0362-546X(98)00153-9 opening in a new tab
- Language
- en English
- Score (nominal)
- 40
- Score source
- journalList
- Publication indicators
- = 5.000; : 2014 = 1.712; : 2006 = 0.677 (2) - 2007=1.079 (5)

- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/article/UAMbd9fdc1ab54944468b8f269773cfe8e9/

* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perishopening in a new tab system.

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