Boundary value problem
A boundary value problem (BVP) gives the value of a function to be determined or its derivatives at multiple different points, in contrast to an initial value problem which gives the value of a function and its derivatives at one point.
Unlike with IVPs, there is no general Existence and uniqueness theorem for IVPs for BVPs, and they may have no solutions, a unique solution, or infinite solutions on a case by case basis.1
A non-homogenous system has a unique solution if and only if the only solution of the related homogenous system is the trivial solution
Boundary value eigenvalue problem