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Existence and Uniqueness
True-or-False

1 .       An equation has a unique local solution if there is some interval I containing t0 on which there is exactly one solution y. [Hint]

 
 


2 .       If there is a unique solution on I, then there is not a unique solution on any subinterval I. [Hint]

 
 


3 .       A maximal solution is a soultion whose only continuation is itself. [Hint]

 
 


4 .       The concept of uniqueness is closely tied to the local nature of the solution. [Hint]

 
 


5 .       Any continuation of y defined on an interval I, must equal y on this interval. [Hint]

 
 


6 .       The graph of any continuation of y is a subset of the graph of y. [Hint]

 
 


7 .       A solution defined on the whole real line is called a local solution. [Hint]

 
 


8 .       The solution normally means the unique maximal solution. [Hint]

 
 


9 .       Theorem 1 is our local existence and uniqueness theorem. [Hint]

 
 


10 .       Theorem 1 requires the function and the derivative to be continuous on some open rectangle. [Hint]

 
 






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