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On the existence of conjugate points for linear differential systems. (English) Zbl 0744.34013
Sufficient conditions ensuring the existence of conjugate points of the solutions of the linear differential system (*) \(y'=B(x)z\), \(z'=-C(x)y\) are searched for. Here \(B\), \(C\) are symmetric \(n\times n\) matrices of real valued continuous functions and \(B\) is nonnegative definite. Some results obtained by E. Müller-Pfeiffer [Proc. R. Soc. Edinb., Sect. A 89, 281-291 (1981; Zbl 0481.34019)] are extended by the author. Then, by applying the Courant’s variational principle, conditions for the existence of conjugate points relative to (*) are obtained.

MSC:
34A30 Linear ordinary differential equations and systems
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