Talk:Kneser's theorem (differential equations)

Mistake?[edit]

That seems strange. If q(x)>0 then liminf and limsup of x^2 q(x) are nonnegative, so they are >-1/4.--79.111.201.50 (talk) 19:49, 16 December 2008 (UTC)[reply]

You are correct, I fixed the theorem by removing the minus sign. MathMartin (talk) 15:39, 17 December 2008 (UTC)[reply]

Not sure what the above was about but it looks wrong now: for q(x)=-1 the solutions are oscillating while for q(x)=1 they are hyperbolic (exponential) and not oscillating. AlexFekken (talk) 07:53, 31 December 2011 (UTC)[reply]

The simplest change to make this consistent with what I found elsewhere and with the counter examples is to swap the inequalities. But I think it is cleaner to get rid of all the minus signs (and swap lim inf and lim sup at the same time). After my edit the contents is now consistent with the obvious counter examples and with http://books.google.com.au/books?id=aBgFYxKHUjsC&pg=PA1103&lpg=PA1103&dq=Kneser+oscillation+theorem&source=bl&ots=bKfxQSIdPC&sig=aRff331x0ypVa1Xf-_oLfyOInlc&hl=en&sa=X&ei=ycL-TsTGN8-aiAeLr5WqAQ&ved=0CEIQ6AEwBA#v=onepage&q=Kneser%20oscillation%20theorem&f=false. AlexFekken (talk) 08:26, 31 December 2011 (UTC)[reply]

I have just added an OR example to help verify in which direction the signs and inequalities need to go. Since this is 'the' obvious example, given the conditions of theorem, I expect and hope that somebody might be able to find it somewhere in the literature and provide a reference. AlexFekken (talk) 11:07, 3 January 2012 (UTC)[reply]

But it can be found in both references given? However, both references use the previous convention with a minus in front of the second derivative. This seems to be more common in Sturm-Liouville theory. --Mathuvw (talk) 17:29, 7 January 2012 (UTC)[reply]

Thanks for pointing that out. But I don't have the reference works, so I didn't know, otherwise I would have made the notation consistent with them. Anybody with access to those works feel free to improve.

Hopefully checking against the example will make it easier to avoid the sort of error in the statement of the theorem that prompted me to make these changes, and add the example, in the first place. AlexFekken (talk) 08:59, 9 January 2012 (UTC)[reply]

Article title[edit]

I suggest that the title of this article ought to be Kneser's theorem, on general grounds, or preferably Kneser's theorem (differential equations) to distinguish it from Kneser's theorem (combinatorics). Deltahedron (talk) 18:21, 26 June 2012 (UTC)[reply]

Done. Deltahedron (talk) 20:02, 2 August 2012 (UTC)[reply]