Vol. 66, No. 1, 1976

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Oscillation criteria for second order self adjoint differential systems

Garret J. Etgen and James Pawlowski

Vol. 66 (1976), No. 1, 99–110

Let be a Hilbert space and let = (,) be the Banach algebra of bounded linear operators from to with the usual operator norm. Let 𝒮 be the subspace of consisting of the self adjoint operators, and consider the second order differential system

Y′′ + P(x)Y = 0

on R+ = [0,), where P : R+ →𝒮 is continuous. Let 𝒢 be the set of positive linear functionals on . The elements of 𝒢 are used to derive oscillation criteria for this differential system. These criteria include a large number of well-known oscillation criteria for corresponding matrix differential systems and scalar equations. Extensions of the results to nonlinear differential systems and differential inequalities are also discussed.

Mathematical Subject Classification 2000
Primary: 34G05, 34G05
Secondary: 34C10
Received: 9 March 1976
Published: 1 September 1976
Garret J. Etgen
James Pawlowski