More bounds for eigenvalues |
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Authors: | William B Day |
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Institution: | Auburn University, Auburn, Alabama 36830 U.S.A. |
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Abstract: | A method introduced by Leighton J. Math. Anal. Appl.35, 381–388 (1971)] for bounding eigenvalues has been extended to include problems of the form ?y″ + p(x) y = λy, when p(x) ? 0 on 0, 1]. The boundary conditions are the general homogeneous conditions y(0) ? ay′(0) = 0 = y(1) + by′(1), where 0 ? a, b ? ∞. Upper and lower bounds for the eigenvalues of these problems are obtained, and these bounds may be made as close together as desired, thereby allowing λ to be estimated precisely. |
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