1
vote
1answer
55 views

Solving Bessel-like equation by using Bessel Kernel [closed]

Consider the drifted-Bessel equation as follows. \begin{equation} x^2\ddot y + x\dot y + (x^2-n^2)y=f, \end{equation} where $n$ is an integer and $f$ is a known function. If $f\equiv 0$, the solution ...
3
votes
1answer
439 views

A name for PDE systems which are neither under- nor overdetermined?

The concepts of overdetermined and underdetermined PDE systems are well known. However, all sources I have so far looked into appear to avoid giving any name to PDE systems which are neither ...
1
vote
0answers
249 views

Differential operator with image of its Frechet derivative in the nullspace of operator adjoint?

Is there an example of a differential operator $A(z)$ with parameter $z \in \mathbb{R}^d$ and Frechet derivative $A_z(z)$ such that $\mathrm{im}(A_z(z)) \subseteq \mathrm{ker}(A^T(z))$. Can this still ...