"A boundary-value problem is a differential equation subjected to constraints called boundary conditions."
ODEs where the values of the dependent variable are given at two or more distinct points.
"Boundary value problems arise in several branches of physics as any physical differential equation will have them."
"Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems."
"A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems involves the eigenfunctions of a differential operator."
"To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input."
"Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed."
"Among the earliest boundary value problems to be studied is the Dirichlet problem, of finding the harmonic functions (solutions to Laplace's equation)."
"A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions."
"Boundary-value problems are differential equations subjected to constraints called boundary conditions."
"The analysis of these problems [Sturm-Liouville problems] involves the eigenfunctions of a differential operator."
"Boundary value problems arise in several branches of physics as any physical differential equation will have them."
"A boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input."
"Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed."
"Among the earliest boundary value problems to be studied is the Dirichlet problem, of finding the harmonic functions (solutions to Laplace's equation)."
"Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems."
"A boundary-value problem is a differential equation subjected to constraints called boundary conditions."
"Boundary value problems...involve the eigenfunctions of a differential operator."
"A large class of important boundary value problems are the Sturm–Liouville problems."
"Boundary value problems arise in several branches of physics as any physical differential equation will have them."
"A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions."