Multiparameter Sturm–Liouville Problems with Eigenparameter Dependent Boundary Conditions

AbstractA system of ordinary differential equations,−y″j+qjyj=∑k=1nλkrjkyj,j=1,…,n,0.1with real valued and continuous coefficient functions qj,rjk is studied on [0,1] subject to boundary conditionsy′j0yj0=cotβjandbjyj1−djy′j1=eTjλcjy′j1−ajyj10.2for j=1,…,n. Here ET=[e1e2···en] is an arbitrary n×n matrix of real numbers and ωj=ajdj−bjcj≠0. A point λ=[λ1···λn]T∈Cn 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