The existence-theorems tag has no wiki summary.
5
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0answers
193 views
When does a “stable” assignment of buyers into goods exist?
Consider a setting of $n$ buyers and $m$ goods.
We have a value matrix $V\in[0,1]^{n\times m}$ specifying how much each buyer values each good (everything is open information here and there is no ...
0
votes
0answers
137 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
votes
1answer
100 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
votes
1answer
149 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
votes
0answers
42 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
votes
0answers
112 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 ...
15
votes
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. ...
4
votes
2answers
675 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 ...
6
votes
3answers
711 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 ...
0
votes
1answer
409 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 ...
19
votes
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 ...
