scholarly journals Minimal periods for ordinary differential equations in strictly convex Banach spaces and explicit bounds for someLp-spaces

2014 ◽  
Vol 256 (8) ◽  
pp. 2846-2857 ◽  
Author(s):  
Michaela A.C. Nieuwenhuis ◽  
James C. Robinson ◽  
Stefan Steinerberger
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Banach Spaces ◽  
Strictly Convex ◽  
Explicit Bounds ◽  
Strictly Convex Banach Spaces

MAZUR–ULAM PROPERTY OF THE SUM OF TWO STRICTLY CONVEX BANACH SPACES

2015 ◽  
Vol 93 (3) ◽  
pp. 473-485 ◽  
Author(s):  
JIAN-ZE LI
Keyword(s):  
Banach Spaces ◽  
Equivalent Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Extension Problem ◽  
Isometric Extension ◽  
Strictly Convex ◽  
Necessary And Sufficient ◽  
Strictly Convex Banach Spaces ◽  
Equivalent Conditions

In this article, we study the Mazur–Ulam property of the sum of two strictly convex Banach spaces. We give an equivalent form of the isometric extension problem and two equivalent conditions to decide whether all strictly convex Banach spaces admit the Mazur–Ulam property. We also find necessary and sufficient conditions under which the $\ell ^{1}$-sum and the $\ell ^{\infty }$-sum of two strictly convex Banach spaces admit the Mazur–Ulam property.

scholarly journals Approximation methods and the generalised Fuller index for semi-flows in Banach spaces

1986 ◽  
Vol 29 (3) ◽  
pp. 299-308 ◽  
Author(s):  
A. J. B. Potter
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Functional Differential Equations ◽  
Periodic Points ◽  
Approximation Methods ◽  
Functional Differential ◽  
Linear Differential ◽  
Fuller Index

In [3] Fuller introduced an index (now called the Fuller index) in order to study periodic solutions of ordinary differential equations. The objective of this paper is to give a simple generalisation of the Fuller index which can be used to study periodic points of flows in Banach spaces. We do not claim any significant breakthrough but merely suggest that the simplistic approach, presented here, might prove useful for the study of non-linear differential equations. We show our results can be used to study functional differential equations.

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