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0answers
127 views

Does there exist this special kind of homeomorphism?

Let $A,B\subset\mathbb{R}^n, n\geq 2,$ are two different shaped spindles. One is thick and one is thin. (Sorry for my unprofessional statements. Unsure about how to say it rigorously.) So there are ...
2
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1answer
94 views

$L^\infty_\mathrm{loc}$ assumption in global existence for Boltzmann equation

In short: In P. Gérard's paper on the existence of global solutions to the Boltzmann equation from 1988 (or equivalently Cercignani's book), why are the stated assumptions (especially $A_n \in ...
2
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1answer
128 views

Global Solutions of Ordinary Differential Equations

Background Let $f: [0, \infty) \times {\mathbb R}^n \rightarrow {\mathbb R}^n$ be a jointly measurable function satisfying, $f(t, \cdot)$ is locally Lipschitz for every $t \geqslant 0$, for every ...
2
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0answers
41 views

reference on existence result for nonlinear elliptic PDE

During my work, I came to the question of existence of weak solutions to the following elliptic equation $$\triangle u + \partial_{1} u + \partial_2(f(x_1,x_2,u)) = 0 \hbox{ in } \Omega$$ with ...
2
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0answers
93 views

Existence and uniqueness of heteroclinic orbits

I am looking for conditions on a nonlinear dynamical system $\frac{d\vec{x}}{dt} = \vec{F}(\vec{x})$ that guarantee the existence of a unique heteroclinic orbit between a stable attractor of this ...
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12answers
1k views

Instances where an existence result precedes the constructive version

The basic motivation here is to encourage and inspire - via examples - the pursuit of alternate proofs of existing results that might be more accessible and intuitive by cataloging success stories. ...
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2answers
656 views

Are there cusp forms for the full modular group Sp(2,Z) and representations det^3 \otimes Sym^2j(\rho_standard)

What are modular forms or cusps forms, resp. ? We start with defining their common domains $\mathbb{H}_g$ as the set of symmetric $g \times g$ matrices with positive definite imaginary parts. The ...
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3answers
671 views

Existence of Rational Orthogonal Matrices

Question: Let $A\in\mathbb{R}^{n \times n}$ be an orthogonal matrix and let $\varepsilon>0$. Then does there exist a rational orthogonal matrix $B\in\mathbb{R}^{n \times n}$ such that ...
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1answer
404 views

Continuous variation from solution of easy problem to solution of hard problem

I asked this question a week ago over on math.stackexchange and got no reply, so I am asking here with slightly different wording. I am trying to prove that there exists a solution to a problem. I ...
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3answers
2k views

Is this 1974 claim still valid?

In G. F. Simmons' Differential Equations book (p.141), the following claim is made: “... As a matter of fact, there is no known type of second order linear differential equation- apart from those with ...