AN OSCILLATION THEOREM FOR SELF-ADJOINT DIFFERENTIAL-SYSTEMS AND AN INDEX RESULT FOR CORRESPONDING RICCATI MATRIX DIFFERENTIAL-EQUATIONS

The main result of this paper is an oscillation theorem on linear self -adjoint differential systems and a corresponding eigenvalue problem. It establishes a formula between the number of focal points of a so-ca lled conjoined basis of the differential system on a given compact int erval and the number of eigenvalues which are less than the given eige nvalue parameter. It extends an earlier result of the author and gener alizes an oscillation theorem of M. Morse. Among others the proof of t he theorem requires a formula on the index of the difference of symmet ric solutions of a corresponding Riccati matrix differential equation. This index formula is the other new result presented.