Abstract
A one-dimensional Sobolev-type inequality supplemented by a Prüfer transformation argument is used to derive upper and lower bounds for the eigenvalues of regular, self-adjoint second-order eigenvalue problems. These inequalities are shown to have applications to counting eigenvalues in the intervals $\scriptstyle (-\infty,\lambda]$, estimating eigenvalue gaps, Liapunov inequalities, and de La Valée Poussin-type inequalities.
Citation
R. C. Brown. D. B. Hinton. Š. Schwabik. "Applications of a one-dimensional Sobolev inequality to eigenvalue problems." Differential Integral Equations 9 (3) 481 - 498, 1996. https://doi.org/10.57262/die/1367969967
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