# Questions tagged [differential-equations]

Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.

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### Determinant of 2D non-positive second order partial differential operator

If I have an ordinary second order differential operator the Gelfand-Yaglom method is often useful to calculate its (regularized) determinant. The great advantage is that one doesn't have to calculate ...
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### Integral inequality implies majorization by solution of ODE

Let $f:[0, \infty)\to [0, \infty)$ be non-increasing (and not necessarily differentiable nor continuous) and satisfy $$f(t)\leq f(0)-C\int_{0}^{t}f(s)^{1/2}ds,$$ where $C>0$. How can one show that ...
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1 vote
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### Continuity in the uniform operator topology of a map

I have a question concerning the continuity for $t>0$ in the uniform operator topology $L(X)$ of the following map: $$t\mapsto A^\alpha R(t)$$ where A is the infinitesimal generator of an analytic ...
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### How to find the maximum value of the following difference equation without using iterative method？

$E(i+1)=(I-AT)E(i)+1/2(AT)^2$ How to find the maximum value of $E$ in this expression without using the iterative method? An approximate estimation is also acceptable. Only the $E$ vector is unknown, ...
I need to solve the following equation: $$y'(t)+2[\cos y(t)+\Omega(t)]=0,$$ where $$\Omega(t)=-2\eta +\frac{2(\eta^2-1)}{\eta-\cos(4\sqrt{\eta^2-1}t)}$$ with $\eta>1$. Undoubtedly, the differential ...
I have the following differential equation $\nabla_\omega \psi=\varphi$ where $\nabla_\omega(\psi)=d(\psi)+\omega(z)\wedge\psi$. With the local coordinates of $y=z-x_i$ the series expansions is  \...