k -component disconjugacy for systems of ordinary differential equations

Johnny Henderson

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-8

Abstract:

Disconjugacy of the k th component of the m th order system of n th order differenttal equations Y ( n ) = f ( x , Y , Y ′ , … , Y ( n − 1 ) ) , (1.1), is defined, where f ( x , Y 1 , … , Y n ) , ∂ f ∂ y i j ( x , Y 1 , … , Y n ) : ( a , b ) × R m n → R m are continuous. Given a solution Y 0 ( x ) of (1.1), k -component disconjugacy of the variational equation Z ( n ) = ∑ i = 1 n f Y i ( x , Y 0 ( x ) , … , Y 0 ( n − 1 ) ( x ) ) Z ( i − 1 ) , (1.2), is also studied. Conditions are given for continuous dependence and differentiability of solutions of (1.1) with respect to boundary conditions, and then intervals on which (1.1) is k -component disconjugate are characterized in terms of intervals on which (1.2) is k -component disconjugate.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:764748

DOI: 10.1155/S0161171286000467

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