On the existence of nonsimple real eigenvalues for general Sturm-Liouville problems
Abstract: The Sturm-Liouville eigenvalue problem , , where is required to satisfy a pair of homogeneous separated boundary conditions at , is considered when no sign restrictions are imposed upon the coefficients , . It will be shown that the general eigenvalue problem above can admit at most finitely many nonsimple real eigenvalues (in some cases none at all). Moreover, we will show by means of an example that nonsimple real eigenvalues may occur in the case when each of and changes sign in and under Dirichlet boundary conditions.
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- R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 1, Interscience, New York, 1953. MR 0065391 (16:426a)
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- R. G. D. Richardson, Contributions to the study of oscillation properties of the solutions of linear differential equations of the second order, Amer. J. Math. 40 (1918), 283-316. MR 1506360
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Keywords: Sturm-Liouville problems, nonsimple eigenvalues
Article copyright: © Copyright 1983 American Mathematical Society