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On the Existence and Uniqueness of Solutions of Ordinary Differential Equations on the Levi-civita Field
| Content Provider | Semantic Scholar |
|---|---|
| Author | Shamseddine, Khodr |
| Copyright Year | 2005 |
| Abstract | The solution of an ordinary differential equation with constant coefficients on the Levi-Civita field is investigated. Contrary to the real case, we first show that even when the order of the equation is finite, it has infinitely many linearly independent solutions; moreover, any corresponding initial value problem has infinitely many solutions. The problems mentioned above are due to the disconnectedness of the field in the order topology and to the existence of nontrivial field automorphisms, and they can be solved by restricting the solutions to analytic functions. We show that an mth order ordinary differential equation with constant coefficients has exactly m linearly independent analytic solutions and that a given initial value problem has a unique analytic solution. AMS Subject Classification: 26E30, 12J25, 11D88. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.wiu.edu/users/kms117/Publications/RSPSDE01.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
