Kamenev type theorems for second order matrix differential systems

Lynn H. Erbe, Qingkai Kong, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


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 ∈ [t0, ∞) (P(t) > 0, t > t0). 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 languageEnglish (US)
Pages (from-to)957-962
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number4
StatePublished - Apr 1993
Externally publishedYes


  • Matrix differential system
  • Oscillation theory
  • Riccati equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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