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Trying to learn math :)


Sep
24
awarded  Autobiographer
Sep
24
accepted How many solutions does the equation $2i+j+3k=l$ have in nonnegative integers?
Sep
24
comment How many solutions does the equation $2i+j+3k=l$ have in nonnegative integers?
thanks a lot for this nice answer!
Sep
21
accepted self-adjoint operator without eigenvalues?
Sep
21
asked How many solutions does the equation $2i+j+3k=l$ have in nonnegative integers?
Sep
18
comment critical points, differential equation
To linearise you take derivative, or the so called Jacobian, and then evaluate the equilibrium point $(x,y)=(a,b/a)$. You can try it yourself and then ask if you have problems.
Sep
18
comment critical points, differential equation
there you go then.
Sep
18
answered critical points, differential equation
Sep
18
comment Proving that maximal interval of existence exists and that solution is unque
Is Gronwall's inequality useful? encyclopediaofmath.org/index.php/Gronwall_lemma
Sep
15
revised Stability analysis for a system of two differential equations
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Sep
15
comment Sketch solution curves
This is the same as math.stackexchange.com/questions/928545/… isn't it?
Sep
15
answered Stability analysis for a system of two differential equations
Sep
12
comment Stability analysis for a system of two differential equations
You need to check the eigenvalues, and eigenvectors (at each equilibrium point), they will give you a local picture near each equilibrium point. Then you might be able to draw global conclusions. Of course everything will depend on the choice of the parameters, so you may have several distinct cases to consider, e.g. all parameters are positive, or all parameters are negative, and so on.
Sep
4
revised self-adjoint operator without eigenvalues?
added 795 characters in body
Sep
4
asked self-adjoint operator without eigenvalues?
Aug
26
comment Every solution of the system is attracted to the center manifold
**tex text is the extension.
Aug
24
comment Every solution of the system is attracted to the center manifold
I made it on Inkscape together with an extension called text ext, which allows you to "write Latex".
Aug
23
answered Every solution of the system is attracted to the center manifold
Aug
8
answered Unique solution to a arbitrary non-linear system under monotonicity assumptions
Aug
8
comment Central manifold theorem => Stable/unstable manifold?
I don't think so, if the centre manifold is of dimension zero, then you have the common results of stable/unstable manifold theory. I must remark though that centre manifolds are very important as the dynamics there are given by the nonlinear terms of your system. Furthermore, centre manifolds are very useful, for example: 1) in singular perturbation problems, or the so called slow-fast systems; 2) In normal form theory; and related to it, 3) In reducing the dimension of the problem you are studying.