Oscillation Criteria Based on a New Weighted Function for Linear Matrix Hamiltonian Systems

Abstract

By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second-order matrix differential system U′=A(x)U+B(t)V, V′=C(x)U−A∗(t)V, where A(t), B(t), and C(t) are (n×n)-matrices, and B, C are Hermitian. These results are sharper than some previous results.