Oscillation problem of Left-Definite Sturm–Liouville Problems with coupled BCs

This paper studies oscillation problems of Left-Definite regular self-adjoint SLPs with real coupled BCs. For a given eigenvalue λ∗λ∗ of the Left-Definite SLPs with real coupled BCs, we conclude that λ∗λ∗ is an eigenvalue of the SLPs with certain separated BCs. We also establish some inequalities among the eigenvalues for the SLPs with separated BCs and coupled BCs. With the help of the obtained results, we give an estimate of the index of eigenvalues and the number of zeros of eigenfunction for the SLPs with real coupled BCs.