k-component disconjugacy for systems of ordinary differential equations
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=1...
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171286000467 |
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| _version_ | 1832560359621263360 |
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| author | Johnny Henderson |
| author_facet | Johnny Henderson |
| author_sort | Johnny Henderson |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fa5ec91befb943ef9d79bdea7b183d58 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fa5ec91befb943ef9d79bdea7b183d582025-02-03T01:27:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019237338010.1155/S0161171286000467k-component disconjugacy for systems of ordinary differential equationsJohnny Henderson0Department of Mathematics, Auburn University, Auburn, Alabama 36849, USADisconjugacy 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.http://dx.doi.org/10.1155/S0161171286000467 |
| spellingShingle | Johnny Henderson k-component disconjugacy for systems of ordinary differential equations International Journal of Mathematics and Mathematical Sciences |
| title | k-component disconjugacy for systems of ordinary differential equations |
| title_full | k-component disconjugacy for systems of ordinary differential equations |
| title_fullStr | k-component disconjugacy for systems of ordinary differential equations |
| title_full_unstemmed | k-component disconjugacy for systems of ordinary differential equations |
| title_short | k-component disconjugacy for systems of ordinary differential equations |
| title_sort | k component disconjugacy for systems of ordinary differential equations |
| url | http://dx.doi.org/10.1155/S0161171286000467 |
| work_keys_str_mv | AT johnnyhenderson kcomponentdisconjugacyforsystemsofordinarydifferentialequations |