### Abstract

We consider the second order matrix differential systems (1) (P(t)Y′)′ + Q(t)Y = 0 and (2) Y″ + Q(t)Y = 0 where Y, P, and Q are n × n real continuous matrix functions with P(t), Q(t) symmetric and P(t) positive definite for t ∈ [t_{0}, ∞) (P(t) > 0, t > t_{0}). We establish sufficient conditions in order that all prepared solutions Y(t) of (1) and (2) are oscillatory. The results obtained can be regarded as generalizing well-known results of Kamenev in the scalar case.

Original language | English (US) |
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Pages (from-to) | 957-962 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 117 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1993 |

Externally published | Yes |

### Keywords

- Matrix differential system
- Oscillation theory
- Riccati equation

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Erbe, L. H., Kong, Q., & Ruan, S. (1993). Kamenev type theorems for second order matrix differential systems.

*Proceedings of the American Mathematical Society*,*117*(4), 957-962. https://doi.org/10.1090/S0002-9939-1993-1154244-0