Applications of a one-dimensional Sobolev inequality to eigenvalue problems

Richard C. Brown, Don Hinton, Štefan Schwabik

Type: Article

Publication Date: 1996-01-01

Citations: 16

DOI: https://doi.org/10.57262/die/1367969967

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.

Locations

Differential and Integral Equations - View - PDF

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