Geodesic
A Note on Klein’s Oscillation Theorem for Periodic Boundary Conditions
Canadian mathematical bulletin, Tome 17 (1975) no. 5, pp. 749-755

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

Recently Howe [4] has considered the oscillation theory for the two-parameter eigenvalue problem 1a 1b subjected to the boundary conditions 2a 2b where for i = 1, 2, — ∞<ai<bi <∞, and qi are real-valued, continuous functions in [ai, bi ], pi is positive in [ai, bi z], and pi (ai )=pi (bi ). Furthermore, it is also assumed that (A1B2—A2B1 )≠0 for all values of x 1 and x 2 in their respective intervals. 
Faierman, M. A Note on Klein’s Oscillation Theorem for Periodic Boundary Conditions. Canadian mathematical bulletin, Tome 17 (1975) no. 5, pp. 749-755. doi: 10.4153/CMB-1974-135-2
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[1] 1. Atkinson, F. V., Multiparameter Eigenvalue Problems, Vol. I, Academic, New York, N.Y., 1972. Google Scholar

[2] 2. Coddington, E. A. and Levinson, N., Theory of Ordinary Differential Equations, McGraw-Hill, New York, N.Y., 1955. Google Scholar

[3] 3. Faierman, M., Asymptotic formulae for the eigenvalues of a two parameter system of ordinary differential equations of the second order, Canad. Math. Bull, (to appear). Google Scholar

[4] 4. Howe, A., Klein’s oscillation theorem for period boundary conditions, Canad. J. Math. 23 (1971), 699–703. Google Scholar

[5] 5. Richardson, R. G. D., Theorems of oscillation for two linear differential equations of the second order, Trans. Amer. Math. Soc. 13 (1912), 22–34. Google Scholar

[6] 6. Stewart, C. A., Advanced Calculus, Methuen, London, 1940. Google Scholar

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