ABSTRACT
The classical Sturm-Liouville eigenvalue problem is, of course, familiar to all of us here. It concerns a differential equation of the form https://www.w3.org/1998/Math/MathML"> − p * y ′ ′ + q * y ≡ λ * w * y https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332623/d03ac290-bd50-452e-ba31-4edd6e078f1a/content/eqn0391.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> on a finite interval [a, b], together with boundary conditions of the form https://www.w3.org/1998/Math/MathML"> A 1 * y ( a ) + A 2 * p ( a ) * y ′ ( a ) ≡ 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332623/d03ac290-bd50-452e-ba31-4edd6e078f1a/content/eqn0392.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> B 1 * y ( b ) + B 2 * p ( b ) * y ′ ( b ) ≡ 0. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332623/d03ac290-bd50-452e-ba31-4edd6e078f1a/content/eqn0393.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> When the coefficient functions p, q, w are nice enough, the differential equation is said to be REGULAR, and it turns out in this case that the eivenvalues of the problem (1), (2), (3) constitute a sequence, λ(n), n = 0, 1, 2, 3, …, https://www.w3.org/1998/Math/MathML"> λ ( 0 ) < λ ( 1 ) < λ ( 2 ) < ⋯ . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332623/d03ac290-bd50-452e-ba31-4edd6e078f1a/content/eqn0394.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
