Klein's Oscillation Theorem for Periodic Boundary Conditions

Howe, A.

Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 699-703

Résumé

Multiparameter eigenvalue problems for systems of linear differential equations with homogeneous boundary conditions have been considered by Ince [4] and Richardson [5, 6], and more recently Faierman [3] has considered their completeness and expansion theorems. A survey of eigenvalue problems with several parameters, in mathematics, is given by Atkinson [1].We consider the two differential equations: 1a 1b where p 1’(x), q 1(x), A 1(x), B 1(x) and p 2’(y), q 2(y), A 2(y), B 2(y) are continuous for x ∈ [a1, b1] and y ∈ [a2, b2 ] respectively, and p1 (x) > 0(x ∈ [a 1, b 1]), p 2(y) > 0 (y ∈ [a 2, b 2]), p 1(a 1) = p 1(b 1), p 2(a 2) = p 2(b 2). The differential equations (1) will be subjected to the periodic boundary conditions. 2a 2b Let us consider a single differential equation

Détail

DOI : 10.4153/CJM-1971-078-8

Bibliographie

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