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Riccati techniques and variational principles in oscillation theory for linear systems. (English) Zbl 0648.34031

The authors consider the second order differential system (1) \(Y''+Q(t)Y=0,\) \(t\in [a,\infty)\), where Y(t), Q(t) are \(n\times n\) real continuous matrix functions with Q(t) symmetric. They present several oscillation criteria for (1). Some of these criteria may be regarded as generalizations to systems of various well-known oscillation tests for the scalar equation \(y''+q(t)y=0,\) \(t\in [a,\infty)\). Two approaches are used in the paper-namely the Riccati integral equation approach and the variational approach, and involve assumptions on the behaviour of the eigenvalues of Q(t) (or of its integral).
Reviewer: J.Ohriska

MSC:

34C99 Qualitative theory for ordinary differential equations
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