International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 373-380
doi:10.1155/S0161171286000467
k-component disconjugacy for systems of ordinary differential equations
Department of Mathematics, Auburn University, Auburn, Alabama 36849, USA
Received 3 October 1985
Copyright © 1986 Johnny Henderson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Disconjugacy of the kth component of the mth order system of nth order differenttal equations Y(n)=f(x,Y,Y′,…,Y(n−1)), (1.1), is defined, where f(x,Y1,…,Yn), ∂f∂yij(x,Y1,…,Yn):(a,b)×Rmn→Rm are continuous. Given a solution Y0(x) of (1.1), k-component disconjugacy of the variational equation Z(n)=∑i=1nfYi(x,Y0(x),…,Y0(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.