INTERVAL OSCILLATION THEORY FOR LINEAR MATRIX HAMILTONIAN SYSTEMS
Abstract
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.
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.
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