# Tagged Questions

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### Prove that the Dirichlet eta function is monotonic

Let us consider $\eta(p):= \sum\limits_{n=1}^\infty \frac{(-1)^{n+1}}{n^p}$ for $p>0$. Has anyone come along with an elementary proof that $\eta(x)$ is monotonically increasing on this set? By ...
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### Caratheodory equations

Ok, I am reading Fillipov book on discontinuous right hand side differential equations (the red book). He states the next lemma: " Let the function $f(t,x)$ satisfy the Caratheodory conditions and ...
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### vector valued BVP for ODE's

I am dealing with a vector valued second order homogeneous BVP: $\ddot u(t) = A(t)\dot u(t) + B(t)u(t)$ with $u(0)=u(1)=0.$ where $A$ and $B$ are $n \times n$ matrices with smooth coefficients and ...
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Suppose that a hypothetical math grad student was pretty comfortable with first-year real variables and algebra, and had even studied some other things (algebraic geometry, Riemannian geometry, ...
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### Functions with “gradients of bounded variation”

Dear all, I would like to know whether the following concept is one that is commonly studied, or has a name, or if there are any textbooks that make reference to it: We say that a function \$f:[a,b] ...