| タイトル | Application of functional analysis to perturbation theory of differential equations |
| 本文（外部サイト） | http://hdl.handle.net/2060/19800017589 |
| 著者（英） | Bogdan, V. M.; Bond, V. B. |
| 著者所属（英） | NASA Johnson Space Center |
| 発行日 | 1980-05-01 |
| 言語 | eng |
| 内容記述 | The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point. |
| NASA分類 | NUMERICAL ANALYSIS |
| レポートNO | 80N26087
JSC-16507
NASA-TM-81073 |
| 権利 | No Copyright |
| URI | https://repository.exst.jaxa.jp/dspace/handle/a-is/172261 |
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