Abstract
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:1a1bwhere p1’(x), q1(x), A1(x), B1(x) and p2’(y), q2(y), A2(y), B2(y) are continuous for x ∈ [a1, b1] and y ∈ [a2, b2] respectively, and p1 (x) > 0(x ∈ [a1, b1]), p2(y) > 0 (y ∈ [a2, b2]), p1(a1) = p1(b1), p2(a2) = p2(b2). The differential equations (1) will be subjected to the periodic boundary conditions.2a2bLet us consider a single differential equation
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