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The Eigenvalues And The Optimal Potential Functions of Sturm-Liouville Operators |
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PP: 125-132 |
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Author(s) |
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Huili Xiang,
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Abstract |
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| In this article, we study the eigenvalues
and potential functions of Sturm-Liouville operators with ordinary
separated-type boundary condition. When the gap of the first two
eigenvalues reaches minimum, we give the specific form of potential
function. Meanwhile, for step potential function, we establish an
one-to-one relationship between the eigenvalues and the nonnegative
real roots of a class of algebraic equation, which provide an
effective method for the approximate calculation of eigenvalues. |
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