Geodesic
Sturm-Liouville Problems Whose Leading Coefficient Function Changes Sign
Canadian journal of mathematics, Tome 55 (2003) no. 4, pp. 724-749

Voir la notice de l'article provenant de la source Cambridge University Press

For a given Sturm-Liouville equation whose leading coefficient function changes sign, we establish inequalities among the eigenvalues for any coupled self-adjoint boundary condition and those for two corresponding separated self-adjoint boundary conditions. By a recent result of Binding and Volkmer, the eigenvalues (unbounded from both below and above) for a separated self-adjoint boundary condition can be numbered in terms of the Prüfer angle; and our inequalities can then be used to index the eigenvalues for any coupled self-adjoint boundary condition. Under this indexing scheme, we determine the discontinuities of each eigenvalue as a function on the space of such Sturm-Liouville problems, and its range as a function on the space of self-adjoint boundary conditions. We also relate this indexing scheme to the number of zeros of eigenfunctions. In addition, we characterize the discontinuities of each eigenvalue under a different indexing scheme.
DOI : 10.4153/CJM-2003-031-0
Mots-clés : Primary: 34B24, 34C10, secondary: 34L05, 34L15, 34L20 
Cao, Xifang; Kong, Qingkai; Wu, Hongyou; Zettl, Anton. Sturm-Liouville Problems Whose Leading Coefficient Function Changes Sign. Canadian journal of mathematics, Tome 55 (2003) no. 4, pp. 724-749. doi: 10.4153/CJM-2003-031-0
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