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Does there exists two differentiable functions $f, g$ on $I$ such that $W(f, g) (x) >0$ on $A$ and $W(f, g) <0$ on $I\setminus A$?
Let $I=(0, 1) $ and $A=\mathcal{C}\cap (0, 1) $ where $\mathcal{C}$ denote Cantor set.
$\color{red}{Question}$ : Does there exists two differentiable functions $f, g$ on $I$ such that $W(f, g) (x) >...
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2
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1
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Does there exist two functions $f, g\in C^1(I)$ for which $W(f, g) (x) >0$ for some $x$ and $W(f, g) (x) <0$ for some $x$?
$f, g\in C^1(I) $ where $I$ is an open interval and $f, g$ both are real valued.
Let $W(f,g)(x) =\begin{vmatrix}f(x) &g(x) \\f'(x)&g'(x)\end{vmatrix}$ denote the Wronskian of $f, g$ at $x\in I$...
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Provide a full phase plane analysis for the model
Provide a full phase plane analysis for the model:
$\left\{\begin{array}{l} \epsilon\dfrac{dx}{dt}=-(x^3-Tx+b)\;,\;T>0\\\dfrac{db}{dt}=x-x_0\end{array} \right.$
So I'm trying to find critical ...
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