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Jun
26
answered Books on Catastrophe Theory
Jun
26
revised Reference about Sobolev spaces
edited body
Jun
25
comment Periodic orbits of “even” perturbations of the differential system $x'=-y$, $y'=x$
The first Lyapunov value is f'''(0)+g'''(0), which is zero, and which also supports your conjecture. It is not difficult for calculate the second Lyapunov value, and maybe even third one. But this is not a proof of course.
Jun
12
comment Lie Groups/Lie Algebra - Applications?
Did you read why Sophus Lie studied continuous transformation groups and their linearizations?
May
9
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
@S.Panja-1729 This theorem exactly answers your question (1). For an answer to questions (2) and (3) you should pick Hartman, ODE.
May
9
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
@S.Panja-1729 See here.
May
9
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
There exists no necessary condition for the uniqueness. Look up Osgood's thorem.
May
8
comment Why did mathematicians name a functional that assigns number to function as a “distribution”?
But you link an article where it is explained why the word "distribution" was used.
May
1
comment Confusion about jump discontinuity and Green's function of a B.V.P.
Two points. First, if you are using (2) you do not need the minus sign ahead of $1/p_0(x)$. Second, the properties of the Green's function can be derived from the definition and properties of the corresponding linear differential operator, you should pick up any textbook on Sturm-Liouville problem.
May
1
comment Confusion about jump discontinuity and Green's function of a B.V.P.
When working with Green's functions, your jumps are defined by your eq. (2) and have sign.
Apr
29
revised Kolmogorov 0-1 law, Measure Theory
added 6 characters in body; edited title
Apr
25
comment Can't argue with success? Looking for “bad math” that “gets away with it”
@JonasMeyer No, the correct limit is 1. you can see it by squeezing the limit between 1 and $(n^1+n^2+\ldots n^n)/n^n$.
Apr
25
awarded  Good Answer
Apr
21
reviewed Reject Vladimir Zorich vs Rudin/Pugh/Abbott
Apr
20
awarded  Yearling
Apr
7
awarded  Good Answer
Apr
6
comment How can we show that for $\lambda <0$ we get the trivial solution $X(x)=0$?
@MaryStar It looks fine to me. To answer your two last questions try to sketch the graphs of $\tan h$ and $1/h$.
Apr
5
answered How can we show that for $\lambda <0$ we get the trivial solution $X(x)=0$?
Apr
4
comment System of first order ODEs with coherent sinusoidal time varying coefficient
@nonlinearism The question deals not with a general case, but with a very specific situation, in which it is reasonable to expect to see more than the general case provides. Your two comments above dismiss the specific form of the problem, referencing very general, but not helpful here, fact.
Apr
4
comment How can one prove the existence and uniqueness of solutions to linear differential equations?
@Ian The solution will be $t^3/3 I$ :) which is of course global.