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Results tagged with ca.classical-analysis-and-odes
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user 33849
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Function approximation via an orthonormal basis (with singular weight)
If you don't mind, please consider the eigenvalue problem
$$ (1-x^2)u''+ \lambda u=0 \ \ \ \forall x\in (-1,1), $$
$$ u(\pm 1) = 0. $$
Observe that for suitable values of $\lambda$, the ODE resembles …
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Accepted
Function approximation via an orthonormal basis (with singular weight)
I hate to answer my own question but since nobody else has ... I now realise that this is essentially a ``singular" Jacobi/Gegenbauer equation ... i.e. it is not technically a Jacobi/Gegenbnauer equat …
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Elliptic Harnack inequality for 1D Schrodinger operator?
There is a nice presentation of Harnack inequalities for linear elliptic p.d.e in Protter and Weinberger "Maximum Principles in Differential Equations". Moreover, there are additional references to th …
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Does this ODE system have solution?
For measurable coefficients, there are existence results available in Coddington and Levinson (originally by Caratheodory, Chapter 2). There are also some interesting uniqueness results there too.
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Does this ODE system have solution?
Let $n=1$. Let $A(t)=1$, $B(t)=0$ and let $c(t)=0$ for all $t\in(0,T)$ for any $T>0$. Then $A(t)$ has an inverse for $t\in (0,T)$. Observe that $u(t)=k$ for all $t\in (0,T)$, for any $k\in \mathbb{R}$ …
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