Initial Value, Boundary Value, and Eigenvalue Problems (continued)

In a Nut Shell: An eigenvalue problem is special type of boundary value problem

(endpoint problem) with an unknown parameter, λ , where the differential equation

has the following form along with the associated boundary conditions:

Type 3: An eigenvalue problem

y ’’ + p(x) y ’ + λ q(x) y = 0

y(a) = A, y(b) = B

where λ is a parameter, the eigenvalues, yet to be determined.

( The goal is to find values of λ that yield nontrivial solutions of the d.e. )

More general eigenvalue problems take on the following form:

Involves more complicated expressions for the boundary value

(endpoint) conditions.

y ’’ + p(x) y ’ + λ q(x) y = 0

a₁ y(a) + a₂ y ’(a) = 0

b₁ y(b) + b₂ y ’(b) = 0

Click here for examples of eigenvalue problems.

Click here to skip to an eigenvalue problem with complicated boundary values.

(Complicated endpoint conditions)

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