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Existence and uniqueness of solutions of ordinary differential equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wend, David V. V. |
| Copyright Year | 1969 |
| Abstract | where II YI I is any norm. For two vectors y = (Yk) and z = (Zk) define y 0 and f(x, y) is nondecreasing in both x and y. Then it is shown that (1.1) has at most one solution to the right of x = xo under the assumptions that f(x, y) is nondecreasing in x and quasi-nondecreasing in y and satisfies an additional condition which prevents any component of a solution from remaining constant. ?3 is devoted to examples illustrating the necessity of some of the hypotheses in the existence and uniqueness theorems. The uniqueness theorem of ?2 generalizes results obtained earlier by the author [3], [4]. |
| Starting Page | 27 |
| Ending Page | 33 |
| Page Count | 7 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-1969-0245879-4 |
| Volume Number | 23 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/1969-023-01/S0002-9939-1969-0245879-4/S0002-9939-1969-0245879-4.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-1969-0245879-4 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
