Multiparameter Sturm-Liouville problems with eigenparameter dependent boundary conditions

A system of ordinary differential equations, -y(j)" + q(j)y(j) = (Sigma(k=1)(n) lambda(k)r(jk)) y(j), j = 1,...,n, with real valued and continuous coefficient functions q(j), r(jk) is studied on [0, 1] subject to boundary conditions y(j)'(0)/y(j)(0) = cot B-j and b(j)y(j)(1) - d(j)y(j)'(1) = e(j)(T)lambda(c(j)y(j)'(1) - a(j)y(j)(1)) (0.2) for j = 1,...,n. Here E-T = [e(1), e(2) (...) e(n)] is an arbitrary n x n matrix of real numbers and omega(j) = a(j)d(j) - b(j)c(j) not equal 0. A point lambda = [lambda(1) ... lambda(n)](T) is an element of C-n, satisfying (0.1) and (0.2) is called an eigenvalue of the system. Results are given on the existence and location of the eigenvalues and completeness and oscillation of the eigenfunctions. (C) 2001 Elsevier Science.