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Oscillation of second order matrix differential systems. (English) Zbl 0993.34034

Here, the author extends some of his oscillation criteria for the second-order Sturm-Liouville differential equation \((p(t)y')'+q(t)y=0\) and the half-linear second-order equation \((p(t)|y'|^{\alpha-2}y')'+ q(t)|y|^{\alpha-2} y=0\), \(\alpha>1\), [J. Math. Anal. Appl. 229, No. 1, 258–270 (1999; Zbl 0924.34026) and in: Ruan, Shigui (ed.) et al., Differential equations with applications to biology. Fields Inst. Commun. 21, 317–323 (1999; Zbl 0924.34025)], to the second-order matrix differential system \((P(t)Y')'+Q(t)Y=0\), where \(Y,P,Q\) are \(n\times n\)-matrices with \(P,Q\) symmetric and \(P\) positive definite. The principal method used in the paper is a suitably modified Riccati method. This modification of the Riccati method is sometimes called \(H\)-function technique.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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