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Results tagged with differential-equations
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user 4362
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
6
votes
Application of bounded spectral theory.
I think Helge's answer cuts to the historical heart of the matter: solution operators for various differential equations tend to be bounded, non-compact operators (obtained in many cases from an unbou …
- 29.2k
5
votes
What does it mean for a differential equation "to be integrable"?
Integrability has a specific meaning for certain differential equations arising in geometry, but I'm not sure if it has a broader meaning for more general differential equations.
Given a collection o …
- 29.2k
11
votes
Will the eigenvalue of the dirac operater tend to negative infinity?
Given any first order, graded, self-adjoint, elliptic operator on a manifold the spectrum is unbounded in both the positive and negative directions. There are probably elementary ways to see this, bu …
- 29.2k
33
votes
Why have mathematicians used differential equations to model nature instead of difference eq...
First, a historical remark: it was not until relatively recently in the history of science that people were convinced that the atomic theory of matter is correct. I believe the tide was turned by a p …