# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Kamenev type theorems for second order matrix differential systems. (English) Zbl 0777.34024
The authors deal with oscillation criteria for self-adjoint differential systems $(*)$ $(P(t)y')'+Q(t)y=0$, where $P,Q$ are $n\times n$ symmetric matrices of real-valued functions and $y$ is an $n$-dimensional vector. As a consequence of the general oscillation criterion for $(*)$ the following result is proved. Theorem. Let $m>2$ be an integer. If $$\limsup\sb{t \to \infty}t\sp{1- m}\lambda \left(\int\sp t\sb{t\sb 0}(t-s)\sp{m-1}Q(s)ds\right)=\infty,$$ where $\lambda(\cdot)$ stands for the largest eigenvalue, then the system $y''+Q(t)y=0$ is oscillatory. If $Q$ and $y$ are scalar quantities then this statement reduces to the oscillation criterion of {\it I. V. Kamenev} [Mat. Zametky 23, 249-251 (1978; Zbl 0386.34032)].
Reviewer: O.Došlý (Brno)

##### MSC:
 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory 34A30 Linear ODE and systems, general
Full Text: