INTERVAL OSCILLATION THEORY FOR LINEAR MATRIX HAMILTONIAN SYSTEMS
Wan‐Tong Li, Sui Sun Cheng · International Journal of Differential Equations and Applications · 2011
By means of Riccati transformation technique and averaging method, interval oscillation theorems are established for linear matrix self-adjoint Hamiltonian system \[ \left\{ \begin{array}{c} U^{\prime }(x)=A(x)U(x)+B(x)V(x), \\[8pt] V^{\prime }(x)=C(x)U(x)-A^{*}(x)V(x), \end{array} \right. \] that are different from most known ones in the sense that properties of $A,B$ and $C$ are only needed on a sequence of subintervals of $[x_{0},\infty )$, rather than on the whole half-line. Examples that dwell upon the importance of our results are also included.