Non-integral criterion for oscillations of linear Hamiltonian matrix systems
The paper deals with the linear Hamiltonian matrix differential systems of the form \[ U'=A(x)U+B(x)V,\;\;V'=C(x)U-A^*(x)V\tag{1} \] under the hypothesis \(A(x), B(x)=B^*(x)>0\), and \(C(x)=C^*(x)\) are \(2\times 2\) matrices of real valued continuous functions on the interval \([a,\infty)\), \(a>-\infty\). Here ``\(^*\)'' stands for the transpose of a matrix. The author presents sufficient conditions (of algebraic type) for the oscillation of the system (1).
scientific article; zbMATH DE number 5077869