Multiparameter Sturm Liouville Problems with Eigenparameter Dependent Boundary Conditions

A system of ordinary differential equations, n yj qjyj Ý krjk yj, j 1, . . . , n, Ž0.1. ž / k 1 with real valued and continuous coefficient functions qj, rjk is studied on 0, 1 subject to boundary conditions yy jjŽŽ00.. cot j and bjyjŽ1. djy jŽ1. eTj Žcjy jŽ1. ajyjŽ1..Ž0.2. for j 1, . . . , n. Here ET e1 e2 en is an arbitrary n n matrix of real numbers and j ajdj bjcj 0. A point 1 n T nsatisfyingŽ0.1. andŽ0.2.is called an eigen alue of the system. Results are given on the existence and location of the eigenvalues and completeness and oscillation of the eigenfunc - tions.