Vol. 32, No. 1, 1970

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Totally positive differential systems

Binyamin Schwarz

Vol. 32 (1970), No. 1, 203–229

Totally positive (TP), and strictly totally positive (STP) differential systems are defined. These real, first order, linear systems are characterized by the form of their coefficient matrices, and by the decrease of the number of sign changes of their solution vectors as functions of the independent variable. A bound is given for the combined number of zeros of the first and last components of any particular solution vector of STP system and a similar result is obtained for TP systems. Examples show that no such bounds exist for the number of zeros of any other component.

Mathematical Subject Classification
Primary: 34.42
Received: 5 June 1969
Published: 1 January 1970
Binyamin Schwarz