Optimality and existence for Lipschitz equations
Solutions of certain boundary value problems are shown to exist for the nth order differential equation y(n)=f(t,y,y′,…,y(n−1)), where f is continuous on a slab (a,b)×Rn and f satisfies a Lipschitz condition on the slab. Optimal length subintervals of (a,b) are determined, in terms of the Lipschitz...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171288000328 |
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| _version_ | 1850163219113443328 |
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| author | Johnny Henderson |
| author_facet | Johnny Henderson |
| author_sort | Johnny Henderson |
| collection | DOAJ |
| description | Solutions of certain boundary value problems are shown to exist for the nth order differential equation y(n)=f(t,y,y′,…,y(n−1)), where f is continuous on a slab (a,b)×Rn and f satisfies a Lipschitz condition on the slab. Optimal length subintervals of (a,b) are determined, in terms of the Lipschitz coefficients, on which there exist unique solutions. |
| format | Article |
| id | doaj-art-ebb5126d38b54db5bc1cf6ce0210bd59 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ebb5126d38b54db5bc1cf6ce0210bd592025-08-20T02:22:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111226727410.1155/S0161171288000328Optimality and existence for Lipschitz equationsJohnny Henderson0Department of Algebra, Combinatorics & Analysis, Auburn University, Auburn, Alabama 36849, USASolutions of certain boundary value problems are shown to exist for the nth order differential equation y(n)=f(t,y,y′,…,y(n−1)), where f is continuous on a slab (a,b)×Rn and f satisfies a Lipschitz condition on the slab. Optimal length subintervals of (a,b) are determined, in terms of the Lipschitz coefficients, on which there exist unique solutions.http://dx.doi.org/10.1155/S0161171288000328 |
| spellingShingle | Johnny Henderson Optimality and existence for Lipschitz equations International Journal of Mathematics and Mathematical Sciences |
| title | Optimality and existence for Lipschitz equations |
| title_full | Optimality and existence for Lipschitz equations |
| title_fullStr | Optimality and existence for Lipschitz equations |
| title_full_unstemmed | Optimality and existence for Lipschitz equations |
| title_short | Optimality and existence for Lipschitz equations |
| title_sort | optimality and existence for lipschitz equations |
| url | http://dx.doi.org/10.1155/S0161171288000328 |
| work_keys_str_mv | AT johnnyhenderson optimalityandexistenceforlipschitzequations |