I forgot about this thread. I had some problem with the last part of this question but found a proof that helped me:
phi denotes the flow.
Let y be in the closure of w(x). Then there exists a sequence y_n in w(x) such that |y-y_n| < 1/2n. Moreover chosoe a sequence s.t t_n --> inf |phi...
Hi all, I have my exam in differential equations in one week so I will probably post alot of question. I hope you wont get tired of me!
Homework Statement
This is Legendres differential equation of order n. Determine an interval [0 t_0] such that the basic existence theorem guarantees a...
Homework Statement
Define the w-limit set (omega) of a point. Show that w(x) is closed.
Homework Equations
The Attempt at a Solution
The definition of a limit set is the set of points to which there exists a sequence t_n→∞ such that \phi(t_n,x) → y
The second question. I was...
Ah yes! I actually tried the triangle inequality but failed. I am going to try again!
Could you please elaborate some more on the second part? I have been stuck on similar questions because I do not understand this argument.
\inHomework Statement
Denote by d(x,A) = inf |x-y|,y \in A, the distance between a point x \in R^n and a set A \subseteq R^n. Show
|d(x,A)-d(z,A)| \leq |x-z|
In particular, x → d(x,A) is continuous
Homework Equations
The Attempt at a Solution
I have no idea on how to prove this. I drew...
Ah, I was thinking right at least. Its so stupid, we don't get any of these rules on our exam so without wiki, I would have never solved this exercise. Thanks for the help.
Homework Statement
Using that the Fourier transform of e^{|x|} is \frac{2}{\xi^2+1}. Compute the Fourier transform of \frac{x}{(x^2+1)^2}
Homework Equations
The Attempt at a Solution
My first thought was to try and rewrite the problem in a form I recognized, tried a couple of things but...