Sturm-Liouville theory

In mathematics and its applications, a Sturm-Liouville problem, named after Charles Francois Sturm (1803-1855) and Joseph Liouville (1809-1882), is a second-order linear differential equation of the form

Related Topics:
Mathematics - Charles Francois Sturm - Joseph Liouville - Differential equation

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:{dover dx}left+q(x)y=lambda w(x)y, (1)

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often together with specified boundary values of y and dy/dx. The value of λ is not specified by the problem; finding the values of λ for which there exist solutions satisfying the boundary conditions is part of the problem. The function w(x) is the "weight" or "density" function.

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The solutions are eigenfunctions of a Hermitian differential operator in some function space defined by boundary conditions.

Related Topics:
Eigenfunction - Hermitian - Differential operator - Function space - Boundary conditions

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Sturm-Liouville theory is important in applied mathematics, where S-L problems occur very commonly, particularly when dealing with linear partial differential equations which are separable.

Related Topics:
Partial differential equation - Separable

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