Recent content by urbanist

Yes, that fraction is the problem. I tried to solve it with l'Hopital's rule, but just got into a recursion, as expected...

Hi all, If we have H'(r)=r+\tau(r)H(r) and \tau(r)=k+(H(r)/r)^a where a>0, k>0, and H(0)=0, can we say anything about {lim}_{r\rightarrow 0^+}\tau(r)? Thanks a lot!

Well, we know that y_1(r)>y_0(r) for all r. If y is defined for all r, isn't it necessarily piecewise continuous? k, at any rate, is continuous. It seems to me that there has to be a neighborhood to the left of r_0 in which y_1(r)-y_0(r)>k(-H_0)H_0-k(-H_1)H_1...

Beautiful solution, once again :) I was wondering, whether the fact that y is not necessarily continuous matters. Can I speak about (H_0-H_1)'(r_0) and y_0(r_0)-y_1(r_0)? Or do I need to deal with (H_0-H_1)'(r\rightarrow r_0^-). And then, can I claim y_0(\rightarrow...

Thanks a lot! That was a very elegant explanation :) Now, can I prove the same for: H'(r)=-y(r)-H(r) k(-H(r)) , where k is a strictly increasing positive function?

Hi all, I'd be very happy if you could help me solve a problem in my research. I need to prove the following: H'(r) = -y(r) - k H(r) k is a constant. y is strictly increasing, but not continuous. Let (a,b]\subset R . (H_x, y_x) denotes solution x. H_1(a)<H_0(a)<0 ...

Thank you so much for your help! I can treat them as coupled. The problem is knowing when to switch from one set of coupled DEs to the other. If I start with w<wm, I'm in the w<wm and H>0 region. This region ends when w>=wm (because H continues to rise). How do I know when this condition...

Hello all, I am dealing with a rather complicated problem (as we all do), without much knowledge in differential equations. I have coded a numerical solution, taking a straightforward approach: constructing the functions step by step, but I would like to try to achieve better precision...