Two-parameter right definite Sturm-Liouville problems with eigenparameter-dependent boundary conditions (Q2710419)

The authors study two-parameter right definite Sturm-Liouville problems of the type NEWLINE\[NEWLINE -(p_i y_{i}^{'})' + q_i y_i = \sum _{j=1}^{2} \lambda_{j}r_{ij}y_{i}, \quad i = 1, 2,\tag{1}NEWLINE\]NEWLINE on \([0, 1]\) with the eigenparameter-dependent boundary conditions NEWLINE\[NEWLINEy_i(0)\cos \alpha_{i} = (p_i y_{i}^{'})(0) \sin \alpha_{i},\qquad(\alpha_{i}\lambda_{i} + b_{i})y_i(1) = (c_i \lambda_{i} + d_i)(p_i y_{i}^{'})(1).\tag{2}NEWLINE\]NEWLINE They obtain existence, location, asymptotics and perturbation results for eigenvalues of some linked Sturm-Liouville differential equations on the unit interval \([0, 1]\), involving two eigenparameters \(\lambda_1\) and \(\lambda_2\), and oscillation results on the eigenfunctions \(y_i\).