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In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form
for given functions , and , together with some boundary conditions at extreme values of . The goals of a given Sturm–Liouville problem are:To find the for which there exists a non-trivial solution to the problem. Such values are called the eigenvalues of the problem.
For each eigenvalue , to find the corresponding solution of the problem. Such functions are called the eigenfunctions associated to each .
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