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| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 1 year, 1 month |
| seen | Jun 14 at 6:36 | |
| stats | profile views | 164 |
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Dec 9 |
accepted | Differential equation, Stability , Lyapunov function |
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Dec 7 |
comment |
Continous function defined by supremum of Radius of disc Wait, we can't claim that we can find u such that $w\in D(z,u) \subset S$. Consider the case when $\delta (z)<|z-w|$ |
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Dec 7 |
comment |
Continous function defined by supremum of Radius of disc Thanks a lot @Travis |
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Dec 6 |
asked | Continous function defined by supremum of Radius of disc |
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Dec 6 |
comment |
Periodic solution of nonlinear differential equation let us continue this discussion in chat |
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Dec 6 |
revised |
Periodic solution of nonlinear differential equation added 6 characters in body |
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Dec 6 |
comment |
Periodic solution of nonlinear differential equation In short, is there any theorem that if the solution of the linearization is periodic, hence the solution of the original nonlinear is periodic too. |
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Dec 6 |
comment |
Periodic solution of nonlinear differential equation More explicitly: Is This argument correct? since $u(t)=A_1\cos(\sqrt{C}t)+A_2\sin(\sqrt{C}t)$ is a periodic solution of$u''(t)+C u(t)=0$, then solution of $2u''(t)+C \sin(2u(t))=0$ is also periodic. |
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Dec 6 |
comment |
Periodic solution of nonlinear differential equation The typo is in the last $z(t)$. the first $z(t)$ is ok. No, we restrict $u(0)\neq 0$. The main point is: Is it true if the linearization system of differential equation have a periodic solution then the original nonlinear have a periodic solution too |
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Dec 6 |
revised |
Periodic solution of nonlinear differential equation edir z' (t) |
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Dec 6 |
revised |
Periodic solution of nonlinear differential equation added 2 characters in body |
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Dec 6 |
asked | Periodic solution of nonlinear differential equation |
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Dec 5 |
answered | Periodic parametric curve on cylinder |
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Dec 5 |
comment |
Differential equation, Stability , Lyapunov function How about this argument: We can reparameterize $S=\{(\sqrt{C}\cos u,\frac{\sqrt{C}}{\sqrt{2}}\sin u, v): u,v\in \mathbb{R}\}$. Let $r(t)= (x(t),y(t),z(t))$ and $r(0)=(x_0,y_0,z_0)$, then $x(t)=\sqrt{C}\cos (t-t_0)$ and $y(t)=\frac{\sqrt{C}}{\sqrt{2}}\sin (t-t_0)$ with $t_0$ satisfying $x_0=\sqrt{C}\cos t_0$ and $y_0=-\frac{\sqrt{C}}{\sqrt{2}}\sin t_0$. Since $z'=xy$ then $z'(t)=\frac{C}{2\sqrt{2}}\sin(2t-t_0)$, hence $z(t)=-\frac{C}{4\sqrt{2}}\cos(2t-t_0)$. Since $r(2\pi)=(x_0,y_0,z_0)=r(0)$ then $r(t)$ is periodic. |
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Dec 5 |
revised |
Parametric curve on cylinder surface added 411 characters in body |
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Dec 5 |
answered | Parametric curve on cylinder surface |
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Dec 5 |
comment |
Differential equation, Stability , Lyapunov function How about the possiblity if the solution only trace the first octan? In this octan, z'=xy>0 so z always increasing. What make you sure that the solution trace along all quadrant of domain |
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Dec 5 |
comment |
Differential equation, Stability , Lyapunov function How about the possiblity if the solution only trace the first octan? In this octan, z'=xy>0 so z always increasing. What make you sure that the solution trace along all quadrant of domain |
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Dec 4 |
accepted | Space of bounded functions is reflexive if the domain is finite |
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Dec 4 |
accepted | Showing that $(X^*)^{**}=(X^{**})^{*}$, where $X$ is a Banach space |
