be real numbers. For any set 
let 
.
takes on at least 
values where 
runs over all 
subsets of 
.
for which 
does not exceed 
.
converge?
satisfying the following two conditions for all 
:![\[ f(x+y)=f(x)+f(y), \;\;\; f \left( \max \{x, y \} \right) = \max \left\{ f(x),f(y) \right\}. \]](http://latex.artofproblemsolving.com/3/9/1/391164166941b57fe54bde43b1f3ef3b49494180.png)
be a closed map with the property that the inverse image of each point in 
is a compact subset of 
.
is compact whenever 
is compact in 
Y by FFA21
Any idea?? Diff equational system combined with Matrix theory.
Consider the equation dX/dt=X^2, where X(t) is an n×n matrix satisfying the condition detX=0. It is known that there are no solutions of this equation defined on a bounded interval, but there exist non-continuable solutions defined on unbounded intervals of the form (t ,+∞) and (−∞,t). Find n.
Consider the equation dX/dt=X^2, where X(t) is an n×n matrix satisfying the condition detX=0. It is known that there are no solutions of this equation defined on a bounded interval, but there exist non-continuable solutions defined on unbounded intervals of the form (t ,+∞) and (−∞,t). Find n.
This post has been edited 1 time. Last edited by c00lb0y, Apr 18, 2025, 7:13 AM
Reason: unsolved yet!
Reason: unsolved yet!
,
.
and true for 
.
.
,
constants: 
.
