Are All Boundary Value Problems Eigenvalue Problems?

[The_Engineer]

Are eigenvalue problems and boundary value problems (ODEs) the same thing?

What are the differences, if any?

It seems to me that every boundary value problem is an eigenvalue problem... Is this not the case?

 

[ShayanJ]

A boundary value problem is a differential equation along with some information about the unknown function like its value in two different points.
An eigenvalue problem is a problem of finding a "thing" which satisfies $Operator ("thing")=nubmer \ "thing"$. Now if the "thing" is a function and the operator is a differential operator,the eigenvalue problem becomes a set of boundary value problems because the number isn't specified and depends on the function.
So,not all boundary value problems are eigenvalue problems and not all eigenvalue problems are boundary value problems.